In many situations, probabilistic predictors have replaced conformal classifiers. The main reason is arguably that the set predictions of conformal classifiers, with the accompanying significance level, are hard to interpret. In this paper, we demonstrate how conformal classification can be used as a basis for a classifier with reject option. Specifically, we introduce and evaluate two algorithms that are able to perfectly estimate accuracy or precision for a set of test instances, in a classifier with reject scenario. In the empirical investigation, the suggested algorithms are shown to clearly outperform both calibrated and uncalibrated probabilistic predictors.