I have no doubt that the police have the ability to trace cell phones. :tongue:
I work for a mobile co, and I used to work for another doing a similar but different job.
At the Old Telco which has a Constant prominent in its name I had access to the records from cell sites for billing disputes "Okay sir, you say you didn't make that call, but you made a call 3 minutes later in the same location to your home number". So can the Police trace where you are or were when you made a phone call? quite probably with a reasonable degree of accuracy if you're in an urban area (more desnely packed transmitters so you have to be closer to them than in the country).
However, its probably going to do you a fat lot of good of your harraser has any sense. I don't know about where you are, but here in the UK if you buy a prepaid (or pay as you go as its sometimes called) sim card you don't even need to register your name. Presuming they havent done something stupid like purchased a contract phone (where they have to give their name for the credit check) or topped up by credit/debit card then they're as good as untraceable.
Your best bet is to actually report this to your telephone company, and the police. The most of telephone cos here in the UK at least have a policy of offering a free phone number change to people who are reporting harrasing calls (limited to one a year or some other reasonable limit). You wont get to pick your number or anything fancy like that, but it kills the calls dead (presuming you dont give the number to the same idiot again). The Police can talk to the Telco's police liason unit (or similar) and get the cell records, account details and topup history.