On the iPhone, go to Settings->General->AirPlay & Handoff and toggle the Continuity Camera off, give it a few seconds, and toggle it back on. That seems to work for a large percentage of users (myself included).
Camera has to have the screen locked, and be in landscape mode. It also has to be stationary; give it 10-15 seconds without motion (verifying that the phone is fixed in place seems to be part of Apple's security setup.) Once it's recognized, the phone can be moved around.