J.H.
I deal with test anxiety. I still have it and I'm in my 30s.
First off, make sure he's studying for tests. Sit with him and help him study. The day of the test, before the test is passed out, have him take a few deep breathes in through his nose and out through his mouth. This gets oxygen to his brain and helps calm him. After the test is passed out, tell him not to turn it over, just to look at the back of it and think about what he studied the day before. Once he's thought about it (just for a few minutes), turn the test over and begin. If he starts to feel stressed or anxiety, tell him to take a few more breathes through the nose and out of the mouth.
If he comes to a question he doesn't remember, then skip it. (I always circle the question number so I can quickly tell what I need to answer.) Once he answers all the ones he knows, then go back and answer the ones he couldn't remember. Tell him not to stress over the answers. If it's a multiple choice, he can eliminate the ones he knows definitely aren't right. Then he can make an educated guess.
Tell him it's ok. There are others out there who have test anxiety too. These are the tips and tricks that help me through it all.
Good luck!