If you're seriously concerned about the security of the information on your phone, you could look at the NSA's Security Configuration recommendations. [1] These recommendations are intended for "Apple iOS 5 Devices", and many of the recommendations sound like they would not be appropriate for the average traveler.
What I would recommend is to keep as much information off your phone as possible. Save emails on your personal computer, and delete them from your phone before traveling. Log out from online accounts like web-based email accounts before traveling. Don't have sensitive files on your phone; encrypt them and download them from a server somewhere that you control.
Finally, as "sumanthvepa" recommended, "keep all interactions with (Border Patrol Agents) on a cordial basis and cooperate immediately and completely when ordered."
[1] https://apps.nsa.gov/iaarchive/library/ia-guidance/security-...
What I would recommend is to keep as much information off your phone as possible. Save emails on your personal computer, and delete them from your phone before traveling. Log out from online accounts like web-based email accounts before traveling. Don't have sensitive files on your phone; encrypt them and download them from a server somewhere that you control.
Finally, as "sumanthvepa" recommended, "keep all interactions with (Border Patrol Agents) on a cordial basis and cooperate immediately and completely when ordered."