The web is full of sites that promise to trace cell phone numbers, but
they all smell of racket and fraud to me.  Is there a reliable way to
trace a cell number (captured from caller ID, person does not return
calls, owes money) reliably?

At this time there is NO reliable or safe method to trace cell phone numbers.
This data is restricted by the various cell phone companies.
The only group that can trace the data are police agencies, usually
requiring a court order. And the FED GOV, who does anything they like.