One stretch that I do is on the tennis court. Just before serving, I lift the left arm up as in a ball toss and hold it stretched for a moment. Then I drop the right arm down with the racquet in hand. Then I bring the racquet to the back scratching position and grab the top with my left hand and pull down. And finally I put the racquet in the position where it would normally strike the ball for the serve and stretch the arm up there. Then I take practice serves.
I have done that for many years and it's gotten rid of any issues related to warming up on serves.
Tennis uses the back muscles a lot and stretching those (I like to grab the back of my knees while sitting on a chair and pull the stomach and chest into the knees) before a match can help to loosen you up.
4 x IG Prestige MP, 70 cm, 376 grams, 386 SW, ALU Power @54, Prince Syn Gut 16 @58