When using a batch means methodology for estimation of a nonlinear function of a steady-state mean from the output of simulation experiments, it has been shown that a jackknife estimator may reduce the bias and mean squared error (mse) compared to the classical estimator, whereas the average of the classical estimators from the batches (the batch means estimator) has a worse performance from the point of view of bias and mse. In this paper we show that, under reasonable assumptions, the performance of the jackknife, classical and batch means estimators for the estimation of quantiles of the steady-state distribution exhibit similar properties as in the case of the estimation of a nonlinear function of a steady-state mean. We present some experimental results from the simulation of the waiting time in queue for an M/M/1 system under heavy traffic. © 2013 AIP Publishing LLC.