On years during which Tisha Be’av falls out on Motza’ei Shabbat, such as this year, 5781, there are three opinions among the Rishonim regarding how Havdala should be recited on a cup of wine on Motza’ei Shabbat.
The first opinion is that of the Geonim who write that one should recite Havdala only at the conclusion of the fast, i.e. Sunday night, before sitting down to eat.
The second opinion is that of the author of the Sefer Ha’Manhig who writes that one should recite Havdala on Motza’ei Shabbat and have a child who is not obligated to fast drink the wine.
The third opinion is that of the Ramban who writes that Havdala is not recited at all, for the Gemara (Berachot 33a) writes that originally Havdala was instituted as part of the Arvit prayer. The, the Jewish nation then became wealthy and our Sages enacted that it be recited over a cup of wine. However, on Tisha Be’av which falls on Motza’ei Shabbat, the entire Jewish nation is considered utterly destitute. The Poskim discuss the varying opinions of the Rishonim at length.
Maran Ha’Shulchan Aruch rules in accordance with the opinion of the Geonim that Havdala should be recited at the conclusion of the fast. We rule in accordance with Maran, whose rulings we have accepted. We therefore customarily recite Havdala at the conclusion of the fast, essentially breaking the fast on wine. Nevertheless, immediately at the onset of the fast on Motza’ei Shabbat, although Havdala is not recited on a cup of wine, one must still recite “Baruch Ha’Mavdil Ben Kodesh Le’Chol” in order to make it permissible to do work.
The “Boreh Minei Besamim” blessing is not recited on a fragrant object at the conclusion of Tisha Be’av, for fragrant objects are not brought to a mourner’s home since they are meant for pleasure. The same applies on Tisha Be’av. Maran Ha’Shulchan Aruch rules likewise.
One must recite the “Boreh Me’orei Ha’esh” blessing on a candle on Motza’ei Shabbat which coincides with Tisha Be’av. It is customary for the rabbi or Chazzan to recite this blessing in the synagogue before the reading of Eicha (although there are those who disagree, see Chazon Ovadia-Arba Ta’aniyot, page 342).
Women who do not attend synagogue on Motza’ei Shabbat must recite the “Boreh Me’orei Ha’esh” blessing on a candle at home (ibid, page 343).
An ill individual who must eat on Tisha Be’av (as we have discussed above) must first recite Havdala on a cup of wine before eating on Tisha Be’av, for one may not eat after Shabbat has ended until one has performed Havdala. The ill individual must therefore recite Havdala on a cup of wine or grape juice and drink it as one would on any Motza’ei Shabbat. An ill individual reciting Havdala on a cup of wine may do so on behalf of the members of his household as he would on any Motza’ei Shabbat and they will fulfill their obligation of hearing Havdala (although they are fasting and the fast has not yet ended).