They'll just imprison you until you unlock the device (or for up to 5 years, if you'd prefer to just wait it out)

Is that per password?

If you are involved in causes frowned upon by the government of the country you are about to enter, you may want to wipe your phone on the plane.

It's more difficult for three letter agencies if you fill the memory with random stuff and encrypt before wiping.

If you don't want your phone used in impersonation while out of your hands, adb shell can be used to take out IMEI, BT and WiFi.

Simpler to just swap mainboards - available on Alixxxx

VeraCrypt has a plausible deniability feature.

May not be tight enough for the NSA but could work for some glorified traffic cops at the airport.

To expand on that, the idea is that a password-protected encrypted volume may have, in its empty space, another password-protected volume, which is indistinguishable from random noise. You can't tell whether it exists or not. Inside that could be another one, and so on.

At least that's the theory, I haven't messed with it to see.

This is a legal problem, not a technical one. If you’re required to turn something over your choice is to do it or sit in jail (or worse if you get the full NYPD/Gitmo treatment).

If you’re really lucky, you can convince them that whatever they’re looking for doesn’t exist but consider how hard it is to prove a negative like that. In most cases, that devolves to the second outcome above, possibly with some destruction of evidence charge.

This is a technical problem, not a legal one. Don't take your phone.

That’s a misattribution. Not bringing your phone means you are choosing not to do something perfectly legal due to abuse of power — and doing so is likely to encourage further abuse because the culprits know they are less likely to be recorded.

I'd disagree, you taking your phone through customs is indeed legal, and the border goon's seizure of you phone (by force if they prefer) and demands for your password on penalty of imprisonment is also legal. So this is not a legal issue, everyone is acting within the law. One could argue that it is a political issue, that the law should be changed (and I'd agree), but that's a different question.

That’s the point: there are multiple laws involved, court cases trying to establish where things like rights to privacy end, etc. – none of those are technical issues.