Verified everything in Joseph's answer, but still no joy getting things set up. Hardware is:
a brand-new 15" MBP with macOS 10.12.3, set up via migration tool from a mid-2012 non-retina MBP with the same OS.
an iPhone 5S with iOS 10.2.1
series 2 Apple Watch with watchOS 3.1.3
I was not prompted to enter my iCloud password after restarting the watch.
The message I get (very quickly) when trying to activate the watch unlock is:
"Your Mac was unable to communicate with your Apple Watch.
Make sure your Apple Watch is unlocked and on wrist, and your iPhone is unlocked."
Related to other suggestions I've seen: I've tried turning hand-off off and back on again on all 3 devices.