Various authors have considered schemes for {\it quantum tagging}, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is potentially unbounded. This task raises some interesting new questions about cryptographic security assumptions, as relatively subtle details in the security model can dramatically affect the security attainable. We consider here the case in which the tag is cryptographically secure, and show how to implement tagging securely within this model.