Risk measurement involves estimating some functional of the distribution of loss. Monte Carlo simulation is often used to estimate the mean of a distribution, but some risk measures, such as tail conditional expectation, are not means of a distribution from which one can sample. This calls for nested simulation, in which risk factors are sampled at an outer level of simulation, while the inner level of simulation provides estimates of loss given each realization of the risk factors. We present a general method for providing a confidence interval for the risk measurement given statistical error at two levels of simulation. The unusual structure of this problem poses a challenge for confidence interval construction and creates opportunities for enhancing the simulation's computational efficiency. We will discuss a specific efficient procedure for estimating a confidence interval for tail conditional expectation.