HUGELY IMPORTANT! I cannot stress that enough. Particularly the younger they are, the more important I feel it is!
My DS was tested by the local university originally. He was just barely 5. They use ed.psych students who are in training to administer the tests. We were told repeatedly that the testers all have experience and training working with gifted children. And they were only going to charge us $75.
The tester had to stop in mid test. She said that my DS refused to answer questions, was uncooperative and had the gall to give me a written report (despite stopping the test!) telling me that he was definitely not gifted and might even need an aide in school to succeed. My DS came out of the room crying, shaken and crushed.
Long story short- my DS asked about 2 min in why there was a mirror on one wall. The tester told him there were people back there watching him. How creepy! A bit later he asked to go to the bathroom and she refused. She also had a timer out on the table, obviously timing stuff but with no explanation. The hardest part for DS was that without any explanation, she would ask him a question, stop mid answer and say "WRONG" and mark the form, then ask again. He just quit completely.
I verified all the above information with her. That was exactly how it went. She didn't really think there was anything wrong with that! Come to find out later, that while many of the testers had experience with gifted children, she was specifically training to work with college students who had ADHD.
DS later tested with a tester who knew her stuff and scored 99.5 percentile... it really does matter.