I competed for 7 years and never got the hang of competing in front of judges. My coaches tried everything- a certain number of stuck routines or skills in a row if I fell on one I would have to start over, going back to basics and drilling them relentlessly, having coaches and teammates watch, every trick they could think of. When I got to meets, my routines were always hesitant and super shaky, my legs shook from the mount to the dismount of my beam routine. Sometimes I would make the big skills and fall on simple ones, have big pauses between connections, or even hit a routine where I looked visibly terrified. I managed a 9.0 on beam once in my entire 7 years of competing. It wasn't unusual for me to score in the 7s for a routine with no falls. I worked with coaches at 3 different gyms and none of them could help me put it together.
So there really is no "one size fits all" remedy for this problem. Some kids will learn to pull it together with a few pressure sets in practice, others will take much more work and a heck of a lot of patience. For the girls who just can't seem to pull themselves together at meets, just offer lots of encouragement, positive reinforcement, and patience. When they are falling apart, just try to calm them down and help them put things in perspective. Remind them of what they know they can do. Reward them for confident attempts, even if they do fall. Also do a ton of the things mentioned above, you never know when it might click. Try having the whole team (not just their level) watch their routines. I know when I was a compulsory level gymnast I was really intimidated by the older optional girls and their coaches and having them watch would have been as bad as a judge!
Having experienced beam anxiety in front of judges to the extreme, I can tell you it's so frustrating to deal with and if not taken care of, can lead to some girls quitting because they feel so dejected about the whole situation. Good luck!