Women and the blessing of Meoreiy Haeish:
Women are obligated in Havdalah. They can either fulfill their obligation through listening to the Havdalah of another person, or through saying it themselves, just as is the law by men. The following will discuss a woman’s obligation vis a vis the blessing of Borei Meorei Haeish.
Are women to say the blessing of Meoreiy Haeish when they say Havdalah?
Some Poskim rule that women are not obligated in the blessing of Meorei Haeish. However, majority of Poskim rule that they are equally obligated just like men, and are hence to say the blessing. Practically, in the event that a woman is reciting Havdalah herself [as opposed to being Yotzei with another] she is to say the blessing of Meorei Haeish during Havdalah, just as is done by a man, and so is the custom. [However, if she is hearing Havdalah from another, it is better for her to be Yotzei with his blessing rather than to say it to herself. Nonetheless, those women who are accustomed to say it to themselves even in such a case have upon whom to rely.]
Are women to place their hands by the fire and look at their nails by the blessing of Meoreiy Haeish?
The custom is that women do not look at their nails upon hearing or saying the blessing of Meoreiy Haeish. Some understand that this is similar to the custom of women not to drink from the wine of Havdalah, and they are hence to be particular not to do so. Nonetheless, they are required to be close enough to the candle to be able to see it and benefit from it at the time that the blessing is said, as is the letter of the law, in order to be Yotzei the blessing.
Women who are saying Havdalah themselves are to likewise say the blessing of Meorei Haeish, just like a man. Women are accustomed not to place their hands and nails near the fire upon saying the blessing, although are required to be within view of the flame, and be close enough to benefit from its light.
 See Admur 296:19; Piskeiy Teshuvos 296:20
 Admur 296:19; 1st opinion in Michaber 296:8
A dispute in this matter is brought in Admur ibid:
First Opinion: Some Poskim rule Havdalah is a Biblical obligation which is learned from the words Zechor…Lekadsho. [Rambam; Chinuch] They expound this verse to mean one must mention the Shabbos both by its entrance and by its leave. Accordingly, also women are Biblically obligated in saying the words of Havdalah just as women are Biblically obligated in Kiddush. This obligation of women towards positive commands of Shabbos is learned from the words Zachor Veshamor, which is expounded to mean that just like women are obligated in the negative commands of Shabbos so too they are obligated in the positive commands of Shabbos. The Sages therefore also obligated women to say Havdalah in Shemoneh Esrei of Maariv and over wine just like the obligation of men, as in these regards both men and women are equally Biblically obligated.
Second Opinion: Others [Rabbeinu Tam; Shivlei Haleket; second opinion in Michaber] rule Havdalah is only of Rabbinical origin, as the words Zachor only refers to remembering Shabbos when it enters and not when it leaves. According to their opinion, some Poskim [Orchos Chaim; Taz] rule women are completely exempt from Havdalah just as they are exempt from all Biblical and Rabbinical positive commands that are time dependent. Now although regarding the laws of Shabbos women are obligated in both Biblical and Rabbinical matters just like men, as since women are Biblically obligated in Shabbos the Sages likewise made them obligated in all the Rabbinical commands related to remembering or guarding Shabbos, nevertheless by Havdalah women are exempt as Havdalah is not a Mitzvah relating to guarding Shabbos but rather an independent matter which the Sages instituted that one separate between the holy and mundane. They supported their institution on a verse in the Torah which states “And to separate between the holy and the mundane.”
Third Opinion: Some [Maggid Mishneh; Meiri; Ritva; First opinion in Michaber] rule that even though Havdalah is of Rabbinical origin, women are nevertheless obligated in Havdalah. Their reason is because in their opinion Havdalah is a Mitzvah relating to the remembrance of Shabbos and its holiness, as in it one mentions the difference between the holiness of Shabbos and the weekday. Therefore, women are Rabbinically obligated in Havdalah just as they are obligated in all matters which the Sages instituted due to the Holiness of Shabbos, as the Sages instituted that their Shabbos laws have the same status as the Biblical Shabbos laws. Thus, just as women are Biblically obligated to remember and guard Shabbos as are men, they therefore are also obligated in all the Rabbinical enactments related to these laws.
The Final Ruling: The main ruling follows the latter [third] opinion, although one is to also suspect for the second opinion. Hence one [whether a man or woman] who has already heard Havdalah is not to say Havdalah for only woman, as according to the second opinion women are not obligated in Havdalah and one is hence saying a blessing in vain. Nevertheless, the women themselves may say Havdalah even according to the second opinion which holds they are not obligated to do so, as a woman may choose to perform with a blessing all positive commands that they are exempt from. [Admur ibid]
 This ruling of Admur ibid follows the ruling of the Bach brought in M”A 296:11; So rules also: M”B 296:35; Peri Chadash; Ashel Avraham Butchach; Siddur Yaavetz; Kitzur SH”A 96:3; Aruch Hashulchan 296:5
Other Opinions: Some Poskim rule that women may not say Havdalah themselves, and are rather to hear someone else say it. [Rama 296:8; Taz 396:7; Kaf Hachaim 296:55; Divrei Yatziv 1:135]
Custom of Sephardim: The Yabia Omer 4:23 rules that according to Michaber women may say Havdalah themselves. However, the Kaf Hachaim ibid concludes that since the matter is under debate women are to be careful to hear half dollar from another person.
 Biur Halacha 296:8 “Lo Yavdilu Leatzman” that so is implication of all Poskim who rule that women are exempt from Havdalah [2nd opinion in Admur ibid; Orchos Chaim; Taz] and so is implication of M”A 296:11 who omits the blessing of Meoreiy Haeish, and furthermore that even according to the opinion that rules women are obligated in Havdalah, it is possible that they agree but nevertheless women are not obligated in the blessing over fire as it is a time dependent blessing which is not essentially relevant to the obligation of Havdalah. The Biur Halacha ibid concludes “it seems more correct to say that according to all opinions women are not obligated in the blessing over fire” [However, see Kaf Hachaim 296:55 From whom it is evident that he learns on the contrary that everyone agrees women are obligated in the blessing over fire.]
 Implication of Admur ibid and all Poskim who conclude that women may say Havdalah themselves and do not mention anywhere that however they are exempt from the blessing over the fire; See all Poskim in next footnote; See Kaf Hachaim 296:55 who seemingly learns that women are obligated in the blessing over fire according to all opinions, even according to the opinions who exempt them from Havdalah;
 Ketzos Hashulchan 96 footnote 12; Daas Torah 296; Ben Ish Chaiy Vayeitzei 22; Kaf Hachaim 296:55 [Seemingly he learns that women are obligated in the blessing over fire according to all opinions, even according to the opinions who exempt them from Havdalah]; Igros Moshe C.M. 2:47; Kinyan Torah 1:88; Vayan Yosef 1:124; Beir Moshe 4:28; Kaneh Bosem 3:17; Sheivet Haleivi 6:42; 7:77; Tzitz Eliezer 14:43; Az Nidbaru 10:27; 11:48; Or Letziyon 2:22-3; Yechaveh Daas 4:27; Teshuvos Vehanhagos 1:266; Moadim Uzmanim 7:255; Piskeiy Teshuvos 296:20; See Nesivos Adam 1:11
The ruling according to the Mishneh Berurah and first opinion: Even according to those Poskim [M”B in Biur Halacha 296 “Lo Yavdilu Leatzman”] who side that women are exempt from the blessing of fire, they are nevertheless permitted to say the blessing as is the law by all Mitzvos that they are exempt from. [Ketzos Hashulchan 96 footnote 12; Implication of Elya Raba 298:3 who rules that this blessing is Birchas Hanehnin; Piskeiy Teshuvos ibid footnote 200] However, see Luach Eretz Yisrael of Harav Tukichisky who writes that they are not to say this blessing themselves and rather to hear it from someone else.
 See Admur 298:20 and 213:6; Michaber 298:13 [and Halacha 11B] that even men should not say the blessings to themselves, due to Berov Am Hadras Melech, and hence certainly here where the matter is under debate if women are obligated in the blessing it is best for them to be Yotzei with another who is anyways saying the blessing; Luach Eretz Yisrael Tukichisky; Piskeiy Teshuvos ibid footnote 201
 See Mateh Efraim 600:4 and Aruch Hashulchan 297:7 bring that it is a vintage custom for the listeners to repeat the blessing of Besamim and Haeish themselves; See Ketzos Hashulchan 96 footnote 8 who explains the reason for this is because according to Tosafus even by Birchas Besamim and Eish the listener must be sitting to fulfill his obligation. Hence to fulfill their obligation according to all, some are accustomed to say it to themselves. Now, according to Admur and majority of Poskim, women are absolutely obligated or at least allowed to say the blessing over fire, and hence there is no need for them to be stringent against following this custom, if it is likewise followed by men of their community.
 Ketzos Hashulchan 96 footnote 12; Piskeiy Teshuvos 296:20
 The Ketzos Hashulchan ibid suggests the reason for this is because before the sin of the tree of knowledge Adam was clothed in nails, and the sin which was caused by Chava caused him to lose these nails and have them remain only on the fingers, therefore they do not look at them. See Piskeiy Teshuvos ibid footnote 202
 Admur 298:21 regarding that the flame must be within view; 298:6 regarding that one may only say a blessing over the flame if he is close enough to the flame to be able to benefit from it and it does not suffice to simply be able to see the flame. Benefiting in this context of Halacha is defined as being close enough to be able to use its light to differentiate between two coins of two different countries.