In location-based services, continuous queries are often employed to monitor the locations of mobile ob-jects that are determined by sensing devices like GPS receivers. Due to limited battery resources, it is impor-tant for these objects to acquire and report location data only if necessary. We study how these energy-consuming operations can be reduced with a con-trolled impact on query accuracy of continuous range queries (CRQs). Specifically, we develop uncertainty-aware tolerances, which are user-defined error bounds that provide correctness guarantees, with considera-tion of different sources of data uncertainty: sensing uncertainty, sampling uncertainty, and communication delay. Novel algorithms are developed to control carefully when an object should acquire and update a location, while satisfying these tolerances. Extensive simulations validate the effectiveness of our methods.