Skin sensitization potential or potency is an important end point in the safety assessment of new chemicals and new chemical mixtures. Formerly, animal experiments such as the local lymph node assay (LLNA) were the main form of assessment. Today, however, the focus lies on the development of non-animal testing approaches (i.e., in vitro and in chemico assays) and computational models. In this work, we investigate, based on publicly available LLNA data, the ability of aggregated, Mondrian conformal prediction classifiers to differentiate between non- sensitizing and sensitizing compounds as well as between two levels of skin sensitization potential (weak to moderate sensitizers, and strong to extreme sensitizers). The advantage of the conformal prediction framework over other modeling approaches is that it assigns compounds to activity classes only if a defined minimum level of confidence is reached for the individual predictions. This eliminates the need for applicability domain criteria that often are arbitrary in their nature and less flexible. Our new binary classifier, named Skin Doctor CP, differentiates nonsensitizers from sensitizers with a higher reliability-to-efficiency ratio than the corresponding nonconformal prediction workflow that we presented earlier. When tested on a set of 257 compounds at the significance levels of 0.10 and 0.30, the model reached an efficiency of 0.49 and 0.92, and an accuracy of 0.83 and 0.75, respectively. In addition, we developed a ternary classification workflow to differentiate nonsensitizers, weak to moderate sensitizers, and strong to extreme sensitizers. Although this model achieved satisfactory overall performance (accuracies of 0.90 and 0.73, and efficiencies of 0.42 and 0.90, at significance levels 0.10 and 0.30, respectively), it did not obtain satisfying class-wise results (at a significance level of 0.30, the validities obtained for nonsensitizers, weak to moderate sensitizers, and strong to extreme sensitizers were 0.70, 0.58, and 0.63, respectively). We argue that the model is, in consequence, unable to reliably identify strong to extreme sensitizers and suggest that other ternary models derived from the currently accessible LLNA data might suffer from the same problem.