Answer
(Fatwa: 1103/937=D/1430)
If you are sure of saliva being transferred to stomach, the sawm (fast) broke and it will render qadha and kaffarah as wajib. But, if you are not sure of saliva being transferred, only it is doubtful, there is neither qadha nor kaffarah.
کما في رد المحتار: والضابط وصول ما فیہ صلاح بدنہ لجوفہ ومنہ ریق حبیبہ فیکفر لوجود معنی صلاح البدن فیہ (الشامي مع الدر المختار، کتاب الصوم باب ما یفسد الصوم وما لا یفسد 2:386)
?The rule is: anything which nourishes the body reaches to stomach, and the saliva of beloved is among them, so one will have to give kaffarah?? (Shami)
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband