There will be a pause in the conversation and (as if its my meeting) I'll say something like generic "Jim what do you think?" No matter what he says I acknowledge it and thank him.
A few things happen. 1. It removes the internal conflict Jim was having if he should speak up or not. 2. It gives him 'the floor' so he knows for a minute he will be heard. Others are probably wondering why I called on him and want to hear what he has to say. 3. His answer might not be directly related, however it often sets off a chain of conversation that often does lead to creative answers.
People actually do like to contribute. The way I look at it is we're not leaving this room until I feel like we have at least heard every idea good or bad. Those set of ideas are our collective intelligence at that moment and I fully intend on leveraging it.