Is there a word for the author of a testimonial about a product or service. I thought perhaps "Testimonee" or something similar but that's not a word.
One who gives testimony, or attests, is an attestant. In your context of "product or service", you might want to also consider "reviewer".
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.