It is human nature to get nervous during a match.
Your best defense against nerves is to stay, or return to, as relaxed a state as possible. There are a few physical things you can do to achieve this relaxed state.
First, take some nice deep breaths just after, as well as, just prior to playing a point. In addition, holding the racquet in your non-dominant hand in between points will give your other arm a chance to relax.
Before a point starts, try gripping the racquet in a very loose and relaxed manor. There should be obvious space between your hand and the grip. Your grip will naturally firm up as you get ready to hit your serve or return serve.
Finally, closing your eyes briefly and trying to focus on just one basic thought (watching the ball is a good one) will help relax your mind, body, and tennis specific muscles and will allow you to perform at your best under pressure.
Steve Annacone, USPTA Elite Pro, is the Director of Annacone Tennis, www.annaconetennis.com and MyHamptonsPro, www.myhamptonspro.com in East Hampton, NY . Steve is also a tennis professional at Ventana Golf and Country Club in Tucson, AZ. In addition, Steve and Miguel Coelho have introduced the JET (Junior Elite Tennis) program at the Tucson Jewish Community Center for high level players ages 8-18. Please contact Steve at email@example.com