A difficult question and one that you really have to answer on your own, but how badly do you need to know who made the call?

If you have been getting nuisance phone calls then you can just report them to your local police station and let them take care of it. If you trust them to pursue it then that should be the matter resolved. Of course if you really want to make sure that someone is going to take action then you need to get in touch with their service provider. The police may not have the power to do anything, but their service provider will take the matter seriously and it could lead to the person making the calls being cut off or worse.

The problem is you can’t phone their service provider without using a reverse cell phone website as without those websites then I don’t know of any other way of identifying who they are with (unless you phone their voicemail and they haven’t changed their message then sometimes you can tell from that). So the best option is really to use one of these sites and dig up the service provider and the details of their name and address.

Then go to the police and report them and give the name and number, then also go to the service provider and report them there too.

That is a double-whammy that ensures the person gets into trouble. Of course they could carry on anyway - but if you know the name of the person you at least have the upperhand and if you let them know you are aware it is them then most people will be too cowardly to carry on when you obviously know it is them.