How to talk about price with a hesitant client without dropping your rate

A prospective client asks for your price. You quote it. There's a pause. They say "that's a bit more than I was hoping" or "let me think about it" or "I'll need to check with my partner."

What you do in the next thirty seconds usually determines whether you win the work, lose the work, or win it at a discount you'll later regret.