I work in Geolocation and do a lot of work resolving questions as to location of devices.
To get back to the original question posted:
"If the police have an email, sent by a suspect over a 3G or 4G network, could they use the IP address (since they know when it was sent) to find out - from the service provider - the precise location the email was sent from?"
If the police have an email, sent by a suspect over a 3G or 4G network, could they use the IP address (since they know when it was sent) to find out - from the service provider - the precise location the email was sent from?
I think the answer can be a lot more specific.
As Mark Buffalo correctly pointed out; 3G/4G Mobile Networks contain ZERO location data associated with the location of the device. So this is a dead end.
The IP ranges are normally assigned randomly to the Mobile Network Provider and relate to that company's locations - not the device. So a UK Mobile Phone customer when roaming in the US would have an IP address that points to somewhere in the UK.
A lot of the other answers seem to relate to the topic of geolocation generally but are not of much help in this case as we only have IP data to work of.
So Mr/Ms Screenwriter, I think you need to try and see if the "Perp" can use a WiFi connection to connect so you get a "static" IP address (rather than the 3G/4G one) which MIGHT help narrow the search down to a town or possibly even a house if the Police could twist some arms amongst the ISP providers.
Or as another person suggested, if you can get the phone number then in countries like the US you can actually track the user without them knowing about it with Cell Tower Triangulation.
However, IP address on a Mobile/Cell/3G/4G connection will not get you anywhere...