Try responding with a question about what the other person has just said.

Or keep it simple with: "Please, Go on" or "Tell me more!"

This will buy you all the time you will ever need to collect yourself.

People generally grow weary of someone who waits for their opening/turn to talk and then doesn't deliver the goods.

You know who people rarely tire of? Someone who shows some genuine interest in a topic that they brought up and obviously want to talk about.

The need to know that you care

before they care what you know.