Slightly off-topic: sometimes cats go out and find a new home especially if your place is too crowded with cats (that is how my parents got an extra cat; he just didn't want to go away). And cats do tend to get themselves killed while crossing a busy street. AFAIK the only way to have some kind of tracking system for a cat is to have a beacon around it's neck which sends out a signal which you can trace. Many cats wear a collar so it is not a no-go as long as it has a weak link so the cat can't hang itself from the collar.
Yes, they don't like crowded places. I agree with them at that and would do the same! I just would do a visit occasionally and eventually after some time congratulate to their new human buddies. Some of my cats found new places to live and I know their locations, it's nice while they feel comfortable at their new place
I'm skeptical about beacons in their neck: Some cats end to be used to them, others are insanely stubborn and always end removing them (most of my cats are even more stubborn than me, figure it!). While cats are smaller, their body is very sensitive and flexible, so many of them prefer to have their body free of any shit.
Would there be another alternative despite it can be surgical? The device needs to be small, inserted in a very easy surgical procedure, very long autonomy (not needing power or using some very low power signal plus one of those peacemaker batteries?) and able to detect location in some way.
I know this is a crazy and difficult idea, but I find current RFID tags useless for finding them.
RFID tags aren't designed to help you find your pet in that way. The idea is, if your pet gets lost, odds are someone will find them. They would then take them to the vet, shelter or pound, who scans them and calls you. Collars can come off (and in fact they should, as they can become snagged, so your pet *should* be able to pull out of them given enough force) which is where an RFID tag is the only way for the authorities to identify them and contact you.
Another benefit of the tags is pet theft. It allows you to unequivocally prove the animal is yours.
There is no way in the foreseeable future to inject an active homing bacon under a dog or cat's skin. Though, radio beacon packs have gotten really small in recent years; you can get them that about the size of a match book now. Battery life is much improved too. (Keep in mind these only use radio direction finders for location. Hunters that run dogs commonly use them.)
There's also cellphone transmitter equipped packs with GPS now. They use geofencing to alert you if your pet goes outside of a defined area. Then they phone home with the current GPS position every 10 minutes or so. Battery life isn't great on them though.
For that last option to really work, you really need something like WiTricity that could charge the unit wirelessly from a distance. Then make the unit completely sealed and ruggedized, maybe even build it all into a neoprene covered collar with flexible PCB materials; perhaps a flexible solar strip on the outside as well, for increased runtime and the ability to self-charge in case your pet *does* get lost (then, once the battery wears down, it goes into standby and only updates every 30 minutes or something).
Aside from the wireless charging, the rest of that technology is very close to being small enough. In fact, if you had a few million to spend on development it may be there already.