What do you say when you have nothing to say?
Nothing!
Silence is not void to be filled. There are moments where words need not to be uttered. There is a difference between silence and awkward silence.
Awkward silence is not a situation where a person runs out of words. For the most part, you find yourself there when you think you need to lead a conversation but you can't find what to say. You feel like you have to entertain the other party, but you can't come up with a cool subject on the fly. If you put yourself in this position, the only way out is to prepare yourself.
One of my favorite speakers is Alain de Botton. But if you've listened to 2 or 3 of his seminars, you've listened to them all. As natural as each of his talks sound, it is the same idea, the same jokes, and all in the same order. He doesn't stutter or run out of things to say because he has rehearsed what he is going to say.
So if you are going to meet someone new, find yourself as a host, find yourself as the entertainer. If you want to carry a conversation, don't wait until you find yourself in an awkward silence. Rehearse.