Bavli, B'rachos 31:2 says (in my own translation):
"Eli answered [Chana], saying 'go to peace'": Rabbi El'azar said, from here we derive, about someone who suspects his fellow of a matter that that fellow is not guilty of, that he must appease him. Moreover, he must bless him, as it says [there], "'and the god of Israel should grant your request'".
And I've heard this cited as practical halacha also (though I have no source beyond the Rosh and the Rif ad loc.): that if someone wrongly suspects an innocent person, he should (or must?) bless him.
Now, I understand that wrong suspicion generally has its root in a lack of empathy or love for the other, and to engender such love one must act in such a way as benefits the other. But why a blessing specifically, as opposed to any other benefit he can bestow on the other, such as a favor or a tangible?
 which I understand is a major teaching of the yeshiva of Navahrudak and its heirs