Is there any way to trace the origin of a private call to a cell phone?

I think I am being harred, and I have suspicions of who it is, bu tthey are calling my cell phone (every day); using a PRIVATE number, so it can't be called back. They are also calling my home phone, but have only called there twice in the last week and hung up. Likewise, they hang up on my cell phone after activating the voicemail. I want to verify who this person is. I called the phone company and they said they can't do it?! I thought they would be able to do it. Is finding out who's calling possible?