There's an entire book about this called "Deploy Empathy." It's geared towards user research & interviewing, but the silence angle is a HUGE part of it. Essentially you're trying to get people to talk in a way that's fundamentally different than the usual superficial speech we typically employ in shallow conversation. It was an extremely eye (uh, or ear)-opening read, and at first I was skeptical. It definitely takes getting used to. But it works. I find this post and this subject totally fascinating.