Anxiety can be caused by a number of factors among them fear of failure or failure of judgment (of self or from others; particularly parents). Fear of failure can be an internal mechanism I see a lot from athletes who are perfectionists who have super high expectations. Or it can come from an external source like fear of letting teammates, parents or coaches down if her performance falls short of those external expectations.
The solution is to keep expectations in check. No matter how old an athlete is there is still so much still to learn and master in the game. Focus her on the things she has control over to minimize her anxiety. From a practical perspective have her work on some deep breathing when she feels the anxiety start in an effort to calm her body down.
As well, since anxiety is a physical reaction caused by a mental thought response to an external stimulus (game situation or interaction) if she can come up with a simple phrase she can tell herself over and over to drown out any negative or fearful thought patterns she has going on that are likely causing the physical response of anxiously she feels. Something like "Have fun," or "You've got this," or "I can do it," or "relax...breathe."
Hope this helps.
You can read some of my articles on the mental game at softballsmarts.com.
Speaking from real life exeriance. My DD has always struggled with in game anxeity since she started playing 10u ball (in practice she would field and hit well, in game she'd freeze). I too thought it was just finding the right saying, more practice, more in game experiance, but nothing worked, it only added pressure. Over the past year, she started battle depression due to a suicide by a classmate (very rough experiance for a 14 yo).
Through the process I learned that depression and axiety go hand in hand with a lot of people. It's a chemical imbalance in the brain, she is now on medication to help with the depression, which also helps the anxiety. She is now doing extremly well in game. In a recent game, as a Varsity Freshman, she faced a D1 commited senior throwing in the high 60's for the first time ever. She was relaxed and took good cuts. Struck out 2 times, but the 3rd at bat was able to get a base hit. In the past, she would have been frozen up there. So the Dr.'s say that she probably has always had some level of depression, but the event made it worse and for her, it was mild depression w/anxiety prior to the suicide.
While I'm not avocating getting everyone on drugs at the first sign of probelms, the anxiety was a underlying sign of a building depression. I just want to raise awareness of the mental health aspect we all as parents face. It's real and its out there and too many parents are ashamed of speaking about it. We are grateful we caught it early enough.