Is there a word for the giver of a testimonial?

One who gives testimony, or attests, is an attestant. In your context of "product or service", you might want to also consider "reviewer".

One who vouches for the quality of some product could be called a voucher, which according to Merriam-Webster is "a person or thing that vouches for the truth of some statement, etc."

Oxford Dictionaries On-Line, gives as its second meaning of referee (after the obvious sporting one):

A person willing to testify in writing about the character or ability of someone, especially an applicant for a job. (It is marked as BRITISH)

A third definition, which is not marked as necessarily British is:

A person appointed to examine and assess for publication a scientific or other academic work.

The second definition, in Britain, would appear to be the one you want. But if you are looking for something American I'm afraid I can't help you.