Trust and verify is a pretty good guideline for working with other people, and it seems to be working pretty well for parenting, too. The trick is to realize that it is TRUST and verify, not pretend to trust and try to catch them out. It almost seems like to separate parts of me are involved: my heart trusts my kids completely, while my brain keeps working on reality checks - not to trap anyone, just to make sure that my trust is still warranted. The good news is that the verifying occurs when I make the effort to stay in touch with my kids. "What did you do last night? Sounds like fun. Who was with you? Oh, good, they're back in town; for how long?" It is just casual conversation (or should be, anyway), because I care about my kids and am interested in what they are up to and who they are hanging out with. But it has the advantage of helping me keep tabs on who they are hanging out with and what they are doing; it gives me a chance to look for discrepancies that might alert me to things I should check on or to places they might need some help or support. And it allows me to trust them because I know that I am checking reality regularly.
Having said that, it works because I really do trust my kids to be honest enough with me that I could catch any discrepancies. The technique breaks down if you have a kid who is determined to keep a secret and willing to lie convincingly and consistently.