The Electronic Frontier Foundation's Rebecca Jeschke sez, "EFF's Jennifer Granick outlines how you should protect yourself while traveling with private data. Bad news: it's not easy."

If you encrypt your hard drive with strong crypto, it will be prohibitively expensive for CBP to access your confidential information. This answer is imperfect for two reasons–one is practical, the other is technological.

Practically, the government has not disclosed CBP's laptop search practices, despite our Freedom of Information Act lawsuit for these documents. We don't know what a border patrol agent will do when confronted with an encrypted machine. One possibility is that the agent will simply give up and let the traveler pass with her belongings. Other possibilities are that the agent will turn the traveler and her machine away at the border, or that he will seize the laptop and allow the traveler to continue on. I suspect that on most occasions, CBP agents confronted with encrypted or password-protected data tell the owner to enter the password or get turned away, and the owner, eager to continue her voyage or to return home, simply complies.

If you don't want to comply, CBP cannot force you to decrypt your data or give over your password. Only a judge can force you to answer questions, and then only if the Fifth Amendment does not apply. While no Fifth Amendment right protects the data on your laptop or phone, one federal court has held that even a judge cannot force you to divulge your password when the act of revealing the password shows that you are the person with access to or control over potentially incriminating files. See In re Boucher, 2007 WL 4246473 (D. Vt. November 29, 2007).