Q. Is it really correct that Horav Shlomo said in a shiur that one may store and save his saliva for use during Yom Kippur to swallow necessary medical pills?
A. Mishna Berura (567: 13), quotes Magen Avrohom that it is permitted to swallow our owns saliva, even though we rule that it is not permitted to drink even liquids that are not fit to drink, swallowing saliva is different, since the intention is not for drinking at all.
Bach (612). cites different opinions regarding how much saliva is one allowed to swallow in Yom Kippur. Chayei Adam (132: 22) and Mateh Ephraim (ibid. 22) maintain that on the onset one should preferably avoid swallowing saliva that has accumulated in the mouth.
Moadim Uzemanim (1: 59) mentions that Hagra'ch Soloveitchik and the Brisker Rov zt'l were extremely careful not to swallow their own saliva when it accumulated during Yom Kippur.
However, many Poskim are lenient and maintain that this is not the accepted tradition. (Beis Meir, Eishel Avrohom Butchatch; 613. Aruch Hasulchan ibid. 4, Piskei Teshuvos 567: 2). Excepting, when particles of food are still in one's mouth. at the beginning of the taanis.
Moadim Uzemanim (ibid.), adds that on Yom Kippur, one should not intentionally accumulate saliva in one's mouth and then swallow it.
Horav Shlomo Miller's Shlit'a opinion is that when in need for swallowing necessary pills, it is permitted to store one's saliva even in a cup and save it for use during Yom Kippur.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a