This is a difficult & tricky situation. On the one hand, you want to set limits for her especially for unacceptable behaviors. On the other hand, she is becoming a young adult, and you have to respect the fact that she will be making her own decisions over time...regardless of whether they are good ones.
The main thing to do is try to establish a dialog with her. You want to know about her relationship with him. You want to know about her thoughts, feelings, and opinions on sexuality. Even if you think she should wait till she's 18 or married to have sex, she may not agree. I assume when you want to "trust them to do the right thing" you mean not having sex or going to quickly physically.
But you are not best friends, you are parent/child. This dialog can be hard to establish openly at your daughter's age...especially because it is a normal part of development for people her age to start connecting more with their peer group than their parents.
The down side of forcing a break up is that it may make things worse. She may then start to see him behind your back & lie to you about it. I think you are better off acknowledging her choices in life, but leaving certain limits. For example, they can go to dinner and see a movie, but most be back by a certain time.
Or he can come over to spend time with her in the house...where you will be in the other room (giving them some privacy but also able to keep an eye on them).
Consider offering her the chance to see a therapist if she needs an objective adult to talk to, or see one together as a family (this is good because it sends the message "Let's work on our problems & communication as a family" instead of "You are misbehaving...you have a problem...go see a professional to fix it.")
I hope this helps. Let me know if you have other questions.