Hi!
It's a really good question. I'm sure there are many ways to overcome the nervousness! I've found a method that worked for me, but I cannot say for certain whether it will apply to everyone equally well.
I scheduled my GMAT in the afternoon, on a Monday. I took a day off on Friday, so I had a nice long weekend. I didn't study very much, because I'd already done as much as I could, and I didn't want to start second-guessing my ability to score well. Over the weekend, I did a lot of reading, watching TV, and playing video games. I relaxed as much as I could and started going to bed much later than usual. As a result, I fell asleep when I was tired, and slept until I was ready to wake up!
The night before the test, I went to bed at 2AM and woke up at 11.30AM. Although I was very nervous, I felt fully rested and ready to perform.
Of course, not everyone can be expected to react in a similar way, but I can tell you that I'm glad I changed my sleep schedule around to better accommodate my needs.