There is an obligation to recite Havdallah on Motza'ei Shabbat specifically over a cup of wine. If one does not have access to wine, or if drinking wine causes him to feel sick, he may recite Havdallah over a cup of beer. Beer is suitable for Havdallah because it is an intoxicating beverage, and it can be drunk in the proper Shiur (quantity). One may not use water, tea, coffee or juices for Havdallah, because they are not intoxicating, and one may not use hard liquors, such as scotch or vodka, because one cannot drink the minimum required Shiur of these beverages. Likewise, one may not recite Havdallah over bread.
When Yom Tov falls on Motza'ei Shabbat, we recite Kiddush and Havdallah together over the same cup of wine. If a person does not have wine or cannot drink wine for medical reasons, may he use beer in such a case? As far as the Havdallah is concerned, as we saw, beer qualifies; however, since in this case the cup is used for Kiddush, as well, perhaps beer cannot be used. What is the Halacha in such a case?
The Shulchan Aruch writes that in this case, too, one may use beer in place of wine. Since Halacha allows using beer for Havdallah, it is valid in this instance for the Kiddush, as well.
If one has neither wine nor beer, he cannot recite Havdallah until he gains access to one of these beverages. Is he allowed to eat before reciting Havdallah? Generally speaking, Halacha forbids eating or drinking on Motza'ei Shabbat before reciting or hearing Havdallah. Would is be forbidden to eat or drink if one cannot recite Havdallah due to the unavailability of wine or beer?
Rabbi Moshe Halevi cites two opinions on this matter (listen to audio for precise citation). The first view claims that in such a case, so long as the individual recited the Havdallah in the Shemona Esrei prayer during Arvit, he may eat and drink despite the fact that he cannot recite Havdallah. According to the second position, however, if the individual anticipates having access to wine or beer on the following day, then he must refrain from eating or drinking until he recites Havdallah on Sunday. Halacha follows the second view, requiring that one refrain from eating and drinking in such a case until he recites Havdallah on Sunday. If, however, he feels ill or particularly weak, he may rely on the lenient view and eat and drink.
Summary: If one does not have access to wine for Havdallah on Motza'ei Shabbat, or if he cannot drink wine, he may recite Havdallah over beer, but not over other beverages or over bread. This applies even on a Motza'ei Shabbat that is also Yom Tov, in which case Kiddush is recited over this cup, as well. If one has neither wine nor beer for Havdallah, he cannot recite Havdallah. If he anticipates having access to wine on Sunday, then he must refrain from eating and drinking until he recites Havdallah on Sunday, unless he feels ill or very weak, in which case he is allowed to eat even before Havdallah.
