Tracing a mobile phone's location without GPS
The base stations always know which cell the phone is closest to. Other than that, the movie version of "tracing" is mostly fictional.

Having an active call causes the phone to transmit a lot more, which might help you find its exact location if you were very close, but does not give you any more location information. 

If you are (or are pretending to be) the base station, you can get at the phone's unencrypted IP traffic, which might tell you something. I think the lookups used by Google Play Services for "precise location" (by list of nearest wifi hotspots) is encrypted but it might not be.

A more devious version of location tracking is the Stingray: a portable fake base station. With one of those, you can drive around until you're close to the target phone.