They put you in prison until you hand over the keys. In the UK this is under RIPA. In the US there's probably some law they can kludge to fit - contempt of court or some-such.
What happens in situations like this if you use a hidden volume within an encrypted file using something like Truecrypt, which allows plausible deniability? You've supplied the "password" but the real meaty stuff is still hidden away...
Yes, I understand that, but if you have 2 passwords, each of which unlocks different plaintext within your encrypted conatainer, then theoretically you could never be found out... (but as you saying, assuming the implementation is correct)