If it doesn't already exist someone should make an Iphone and/or android app that will let you lock your phone before you go through customs, and only allow you to unlock it at a specified time and/or place. For instance 5 hours after landing at the location of your booked hotel.
That way you won't be able to divulge information held on your phone, even if you wanted to.
That way you won't be able to divulge information held on your phone, even if you wanted to.