We have now used a local school district psychologist who works on the side doing gifted testing to make extra money. She's very qualified and knows what she's doing and how to write up a report that schools will listen to and understand. We found her by calling local school districts and asking if anyone did private testing.
If you go the university route, please make sure you have the opportunity to talk to the student psychologist and that s/he is familiar with gifted issues. Our unfortunate experience was that it was the worst $75 I've ever spent.
The tester was completely unfamiliar with gifted kids. My DS, who was 5 at the time, was confused about the giant mirror in her office and asked her about it during the testing. The tester told him that there were people back there watching him. He freaked and refused to answer most of her questions.
My now DYS kid ended up with a testing report that said that he was definitely not gifted, had severe learning challenges and would possibly need full-time support in the classroom to function. I can look back and laugh at it now but it was horribly traumatizing for all of us!
Ask questions first :-)