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Location information should be verifiable in order to support new computing and information services. In this paper, we adapt the classical challenge-response method for authentication to the task of verifying an entity's location. Our scheme utilizes a collection of transmitters, and adapts their power allocations to verify a user's claimed location. This strategy, which we call power-modulated challenge response, is able to be used with existing wireless sensor networks, and we present three variations. First, we propose a direct method, where some transmitters are selected to send "challenges" that the claimant node should be able to witness based on its claimed location, and for which the claimant node must correctly respond in order to prove its location. Second, we reverse the strategy by presenting an indirect method, where some transmitters send challenges that the claimant node should not be able to witness. Finally, we present a signal strength based method, where the node responds with its received signal strength and thereby provides improved location verification. To evaluate our schemes, we examine different adversarial models for the claimant, and characterize the performance of our power-modulated challenge response schemes under these adversarial models.