Cloneability of AES-128
Basically, there are two ways of doing this: the symmetric and the asymmetric way. 



For the symmetric way: you put in a secret key, which can be derived from a master key. In that case it makes sense to have a static, unique UID per card, which you can use to derive a key for the tag with the master key. Then that key is put on the card, and you can then create e.g. a challenge-response protocol for it. The inspection system needs to have the master key and do the derivation as well, so to be able to verify the challenge-response.

Of course somebody being able to steal an inspection system and/or retrieve the master key from it is of course the weak point of the system. A lot of these systems have methods of using a new master key / derived key in case a master key gets stolen (and this is detected).



Of course you can also put on a private key and (card verifiable) certificate, signed by a higher level certificate. That way the inspection system can first read out the certificate, verify it using a parent certificate in a trust store, and then again verify a challenge signed with the private key. Of course, a smart card chip costs more than a chip that implements challenge-response, doubly so if it contains a private key - and therefore an asymmetric co-processor (Montgomery multiplier), because these CPU's are too slow and possibly too vulnerable against side channel attacks.

This is the asymmetric way, and it only requires a trusted public key to be present in the inspection system.



As always, with NFC tags or contactless (smart) cards, the more complex / secure the more expensive. Prices quickly go down on higher volumes though.