In most sensing applications, the measurements generated by sensor networks are noisy and usually annotated with some measure of uncertainty. The question that we address in this paper is how to estimate the accuracy of these uncertain sensor measurements. Existing studies on estimating the accuracy of uncertain measurements in real sensing applications are limited in three ways. First, they tend to be application-specific. Second, they typically employ learning techniques to estimate the parameters of sensor noise models, and ignore alternative state estimation approaches without learning. Third, they do not explore whether exploiting the dynamics of the monitored state can yield significant benefits. We address the above limitations as follows: we define the accuracy estimation problem in a general manner that applies to a broad spectrum of application scenarios. We present a general framework to address this problem, and show that the proposed framework can be implemented in a number of different ways. We evaluate and compare the different implementations in the context of two real sensing scenarios, and discuss how they trade accuracy for computation cost, and how this trade-off largely depends on the user's knowledge of the application scenario.