Prediction intervals are needed to quantify prediction uncertainty in, for example, warranty prediction and prediction of other kinds of field failures. Naïve prediction intervals (also known as intervals from the “plug-in method”) ignore the uncertainty in parameter estimates. Simulation-based calibration methods can be used to improve the accuracy of prediction interval coverage probabilities. This article investigates the finite-sample coverage probabilities for naive and calibrated prediction interval procedures for the number of future failures, based on the failure-time information obtained before a censoring time. We have designed and conducted a simulation experiment over combinations of factors with levels covering the ranges that are commonly encountered in practical applications. Our results indicate situations where the naïve prediction procedure performs poorly but where properly calibrated procedures do well. The simulation also uncovered exceptional cases, caused by the discreteness of the number of failures being predicted, where even the calibrated procedure can perform poorly.