Earlier quoted context omitted.
Like, leave a private key at home and encrypt your drive with the public key before crossing the border? Yeah, at that point you are powerless to do anything until you are at home.
But what's the difference? The end result is the same: your device(s) are confiscated and they attempt to brute force the password. Telling an officer that you cannot give them the password because you did some techno-mumbo-jumbo is just going to piss them off and make them assume you have "something to hide" because "no honest person would go to those lengths".
If an LEO (claims to) need access to something and you give him a dead end, it's his job to assume you're lying and find the next legal option available to him.
The real question you should be asking yourselves isn't "How would you outsmart the caveman cop in this situation?" Rather, it's "What can/will you do, as a citizen, to resist the erosion of our civil liberties?" Sadly, I have no easy answers here.