Estimating the reliability of individual classifications is very important in several applications such as medical diagnosis. Recently, the transductive approach to reliability estimation has been proved to be very efficient when used with several machine learning classifiers, such as Naive Bayes and decision trees. However, the efficiency of the transductive approach for state-of-the art kernel-based classifiers was not considered. In this work we deal with this problem and apply the transductive reliability methodology with sparse kernel classifiers, specifically the Support Vector Machine and Relevance Vector Machine. Experiments with medical and bioinformatics datasets demonstrate better performance of the transductive approach for reliability estimation compared to reliability measures obtained directly from the output of the classifiers. Furthermore, we apply the methodology in the problem of reliable diagnostics of the coronary artery disease, outperforming the expert physicians’ standard approach.