Quantiles, which are known as values-at-risk in finance, are often used to measure risk. Confidence intervals provide a way of assessing the error of quantile estimators. When estimating extreme quantiles using crude Monte Carlo, the confidence intervals may have large half-widths, thus motivating the use of variance-reduction techniques (VRTs). This paper develops methods for constructing confidence intervals for quantiles when applying the VRT importance sampling. The confidence intervals, which are asymptotically valid as the number of samples grows large, are based on a technique known as sectioning. Empirical results seem to indicate that sectioning can lead to confidence intervals having better coverage than other existing methods.