I just had the problem where my Mac would say, "Unlocking with Apple Watch," spin for a few seconds, then prompt me with a password. I discovered that the problem was my watch wasn't connected to my wifi. Now, I would argue that it should have worked with just Bluetooth, but whatever. I followed the steps on this page:
http://www.iphonehacks.com/2015/05/how-to-ensure-apple-watch-is-connected-to-a-wi-fi-network.html
And got my watch to connect to Wi-Fi, which it finally did. (I've actually had this problem forever on my home network but just figured my watch was too far away from my router.) Now it works like a champ.
A little bit of info would've been nice, but, then they wouldn't be the Apple we know. :|
Thanks @John6Plus !
My CAT enabled Mac Pro 4,1 (fw upgraded to 5,1) running macOS Sierra can now be unlocked by my Apple Watch.
I had the options selected before, but would never unlock.
Used the link you provided and disabled BT on my phone. My watch went from Disconnected to Connected and could access my Wifi.
Locked my Mac Pro and tested the unlock with my apple watch and it worked successfully.
Appreciate the post greatly - made my day !!