Classification is one of the most important tasks of machine learning. Although the most well studied model is the two-class problem, in many scenarios there is the opportunity to label critical items for manual revision, instead of trying to automatically classify every item. In this paper we adapt a paradigm initially proposed for the classification of ordinal data to address the classification problem with reject option. The technique reduces the problem of classifying with reject option to the standard two-class problem. The introduced method is then mapped into support vector machines and neural networks. Finally, the framework is extended to multiclass ordinal data with reject option. An experimental study with synthetic and real data sets, verifies the usefulness of the proposed approach.