TrueCrypt let you encrypt your drive in a "plausibly deniable" way. One password would let you see the encrypted contents as would expect, but there was also a sort of duress password. If you mounted the drive with the second password, you would not see files added with the "true" password. You could even add files to this file system so it looked like a fully functioning file system.

How would the authorities know you have given them the correct password?

I'm not sure how effective it was, I remember there being some criticism of it.