Consider public speaking. It is one of the most stressfull situations people can have. People rank fear of public speaking above fear of death.
So what is happening as you sit in a chair, waiting to be introduced? Your legs are folded in an unnaturally chair constricted posture that let's your quads shrink, and even atrophy.
These are your fight or flight muscles. When an alligator leaps out of the water these muscles need to fire up and carry you off the field. So your body is telling your mind that you are not ready to move. Your mind, in turn is telling your body that you are about to enter a dangerous situation. It is a feedback loop. You are about to expose yourself with no ability to fight or fly!
The trick I learned at a recent speaking engagement was to loosen these up these tense muscles. You will be cool, calm and relaxed as you speak. Just sit a little forward on your chair, and bend your leg to the floor. The top of your body will be unchanged, so people watching you sit at a table will simply see your upper body and a smile on your face. Meanwhile your quads are loosening allowing you to relax and prepare for a stressful situation.
And...if your speech is not well recieved.
You will be able to fight or fly!