Whilst I received this from a coach colleague and it refers to juniors,
The information is also pertinent to seniors.
In addition - all parents should read this, and apply.
As a young junior player I was always nervous when it was competition time.
My friends would add some extra pressure saying thinks like: "I know this guy;
you should beat him in less than 20 minutes!", "Oh, you'll have an easy match!",
"You beat him all the time in practice; it should be easy this time too!" or "This
guy is number one seed; good luck!" etc. 
Whether you are a tennis player or a tennis parent who doesn't know what to tell
his/her kid before a match, here is my personal suggestions:
You or your children should not play with the outcome (winning or not losing the
match) in mind. That puts, from the beginning, so much pressure on the player.
Consider the upcoming match as something enjoyable and hoping that the result
will be in accordance with your good feeling of playing the game.
Playing every point and loving the competition is a healthy way for a long lasting
experience in sports like tennis. 
- DO YOUR BEST! (with a smile)
Very important is the message that whatever happens on the court, the player
should be proud of the way he/she played at the end of every match. After all,
tennis is a sport and it should be taken like that - there are no victims in sport;
just characters. 
The less a parent talks with his son or daughter before a match the better. The
main thing is that children need to know that the people they love are there for
them and supporting them. 
A confident and caring look, a hand-shake or a pat on the back will do more than
a pep-talk. 
When you watch a match, as a parent, wife, husband or grand-parent of the
player, try to look like you are watching the match attentively. Avoid laughing,
chatting or (worse) yawning during the match. If by any chance the player looks
your way, he/she should see that you are there and caring. 
Things you should NOT tell yourself (if you are a player) or to your kids before a
tennis match:
“- Remember what you practiced!” 
A tennis match is far different than a practice. Whatever you worked on with your
coach should be, by now, muscle memory. Whether there is the mental attitude,
that perfect backhand swing, a kick serve etc. you should not think about the way
you execute them. Your focus should be away from your tennis technique or
footwork; instead you should focus on your opponent: finding weaknesses and
building a strategy that works for you. 
“- You beat her before (you can do it again)!” 
This statement adds more pressure on the player unconsciously telling her that
it is expected from her to win again. 
“- You can win this match!”
Again, the outcome of the match should not be something a player has in mind
from the beginning. That would make the player tense up from the start. 
In conclusion, the less advice the player gets before a match, the better. Keep it
short and very, very POSITIVE.

                                                                 written by:-   Cosmin Miholca
                                                                                         USA Coach