I more or less do this for stealth or deception checks. I get the players to tell me their modifier, and then roll behind the screen. And then I'll give them a description like "try as you might, you can't seem to make your armor stop squeaking" or "to the best of your knowledge, you are quiet and unseen" or whatever. But I don't actually tell them what they rolled, and let the scenario play out.
My players seem to actually prefer this, since it allows them to blissfully ignore the metagaming elements.
Gotta work on your poker face with that one, as DM. Sometimes I can't help but laugh, so I deliver...
(They roll a 2) you believe you are hidden but are in fact betraying your position -- you're the equivalent of clown shoes sticking out from under the barrel. How would you describe this?
A good roleplayer leans into this and hijinx abound.