"Faith" would seem to be historically primarily associated with religion, but, if so, modern usage has shifted its domain of application; it can be seen that the most important context where the word is used is not religion but the context of some sort of belief that can be put into certain facts; the first sense defined in the OALD is that one.
faith 1. [uncountable] trust in somebody’s ability or knowledge; trust that somebody/something will do what has been promised
♦ If the company can retain its customers' faith, it could become the market leader.
faith in somebody/something I have faith in you—I know you'll do well.
♦ We've lost faith in the government's promises.
♦ Her friend's kindness has restored her faith in human nature.
I wouldn't put too much faith in what she says.
♦ He has blind faith (= unreasonable trust) in doctors' ability to find a cure.
It can be seen in the SOED that the word has its general meaning already in Middle English and that it takes o its religious sense only in Late Middle English.
I 1 Confidence, reliance, belief, esp. without evidence or proof (Foll. by in) ME
3 Theol. Belief in the doctrines of a religion, esp. such as affects character and conduct. LME
"Certainty" could be used but the preposition must be changed.
- If negotiations are to prove fruitful, there must not only be sincerity on each side, but there must also be certainty as to the sincerity of the other side.
"Certainty" fails to connote the idea of trust associated with faith; whereas "certainty" implies more factual phenomena, "trust" relies on phenomena that are not so tangible.
The awkwardness felt relative to the idea of "the substance in someone's sincerity" is understandable as sincerity is not a concept that lends itself to being described in terms of substance; it is only the appraisal of a match/mismatch between a stance of an individual and a state of mind of his/hers that is made up of levels, of certitudes/incertitudes, of likes/dislikes, and which, according to how the stance reflects the particular weighs of these opposites, can be considered as categorizing the individual in question as either not very sincere, hypocritical, sincere, very sincere, etc. The concept of substance is foreign to the idea of appraisal: the essence of the idea in the decision about how well founded is this match/mismatch is uniquely that of a judgement.
As shows the most frequent vocabulary on the model "< xxx > of his sincerity", that is the words
"doubt", "pledge", "evidence" and "suspicion",
what matters is the truth of a jugement. The word "evidence" could have been used also.
- If negotiations are to prove fruitful, there must not only be sincerity on each side, but there must also be some evidence of the sincerity of the other side.