RFID (or other) - Proximity Detector
An RFID tag is, in its basic form, a passive device until it is subjected to a localized field (usually magnetic) whereupon the tag's power circuits collect enough energy to form a supply voltage that can activate a small microprocessor and it either modulates the impacting magnetic field (so that the base station can determine the codewords sent by the tag) or it generates an RF field that the base station can receive.

Some tags have batteries but, for the most part they are passive and don't ping an output field that can be detected by a similar tag.

If you want to ping a field you are going to need far more power/energy than that available to a tag and the batteries won't last that long. However, it's not impossible to get several weeks life from a D cell I would imagine - it would need to be carefully designed and quite possibly use infra red pings to see if another animal was close by.

You can locally store "meetings" between the cats in each "tag" and somehow download that information when a cat approaches a base station of some type. This could use regular tag technology I reckon.