In wireless location-aware networks, mobile nodes (agents) typically obtain their positions through ranging with respect to nodes with known positions (anchors). Transmit power allocation not only affects network lifetime, throughput, and interference, but also determines localization accuracy. In this paper, we present an optimization framework for robust power allocation in network localization to tackle imperfect knowledge of network parameters. In particular, we formulate power allocation problems to minimize the squared position error bound (SPEB) and the maximum directional position error bound (mDPEB), respectively, for a given power budget. We show that such formulations can be efficiently solved via conic programming. Moreover, we design an efficient power allocation scheme that allows distributed computations among agents. The simulation results show that the proposed schemes significantly outperform uniform power allocation, and the robust schemes outperform their non-robust counterparts when the network parameters are subject to uncertainty.