In location-based services, continuous queries are often employed to monitor the locations of mobile objects that are determined by sensing devices like GPS receivers. Due to limited battery resources, it is important for these objects to acquire and report location data only if necessary. We study how these energy-consuming operations can be reduced with a controlled 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 consideration 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.