We investigate the problem of verifying location claims of mobile devices, and propose a new property called simultaneous distance modification (SDM). In localization protocols satisfying the SDM property, a malicious device can lie about its distance from the verifiers, but all distances can only be altered by the same amount. We demonstrate that the SDM property guarantees secure verification of location claims with a small number of verifiers even if some of them maliciously collude with the device. We also present several lightweight localization protocols that satisfy the SDM property.