This happened to me crossing into Canada and to be honest I really wasn't expecting it. I had tons of very private pictures and messages on there stretching back years. I really didn't want to turn over my password so that 3 border agents could look through all that stuff in some back room, but at the same time I knew there wasn't anything illegal on there. Anyway, I was with my partner and didn't want to ruin her vacation as well so we just turned over our passwords (under threat of detention if we didn't).
In any case, if you find yourself in this unfortunate situation (you shouldn't - you should travel with an empty phone when crossing the border, or at least wipe it before crossing then do a restore over icloud later), here's something you can do: Before going in (if you have an iphone), make sure you have a strong alphanumeric passcode. Enable auto-wipe on 10 incorrect passcode attempts. Then, turn the phone off. If CBP then asks to turn your phone on and wants your password, appear eager to comply, but give them an incorrect one, and when that doesn't work, admit that you had just changed it a few days ago to something more secure and that you may have forgotten it, but don't worry, you always just use the thumbprint to unlock the phone anyway and volunteer to open it that way. Always appears helpful. The phone still won't unlock because iphone requires passcode entry after restart. If they ask why you turned the phone off, just say that's what you normally do when entering border control. Unless you're under some kind of serious suspicion of some kind at this time, they're unlikely to detain you for forgetting your phone password, and even if so, it's locked with a strong passcode so there's no much they can do anyway.