Actually, they probably have quite a bit of power. They have whatever evidence led to the warrant in the first place. If they don't find something they know you have, they'll know you have given them the wrong password. If your browser history is three months old and contains nothing but chocolate chip cookie recipes, they'll know you have given them the wrong password. I don't know what happens next, but I doubt they'll say "oh, that was sneaky" and let you go.
When Reiser was asked to explain why he hosed out his car and said "everybody loves a clean car", the jury was not particularly impressed.
This amounts to nothing more than suspicion. When we get to the point where their failure to find the incriminating evidence they were searching for is evidence of your guilt, we're by nature already at the point that that evidence was never required anyway, and we're just in a fascist dystopian reality.
Exercise to the reader to ascertain if this has already come to pass.
That's not how you are supposed to use (e.g.) TrueCrypt. Your dummy passphrase, without the incriminating data, should be the one that you use for all legitimate business.
If you have multiple dummies, be sure to have something embarrassing, but not incriminating, in the other dummies.
When Reiser was asked to explain why he hosed out his car and said "everybody loves a clean car", the jury was not particularly impressed.