I think there was a recent court finding about this kind of search.
http://www.slate.com/blogs/future_tense/2015/09/25/court_rules_that_defendants_don_t_have_to_provide_smartphone_passcodes.html
Evidently, current rulings say that a warrant can force you to provide you fingerprint, but not a passcode. A passcode is part of your mind and is protected by your 5th amendment rights.
So the short answer is if you don't want your phone searched, use a passcode, not a fingerprint.
This fingerprint versus passcode stuff is nonsense. The courts may have ruled a fingerprint isn’t the same thing as a passcode, but it’s all based on getting access to documents that may incriminate the person. A person shouldn’t have to give ANYTHING that might incriminate themselves. That includes a blood test in my book, although sensors that measure such external things such as breath are a different matter.
I view the constitution as always putting the greater burden/limit on government. When there’s a question, the benefit of the doubt should go to We the People. Of course, this isn’t how the modern courts often rule, and a Hillary Clinton court will be a rubber stamp for whatever she wants.