On-board diagnosis (OBD) aims at detecting malfunctions of emission-related components of road vehicles. It is required by legislation in United States and the European Union, as it is considered to be beneficial for the reduction of vehicle-related air pollution. On-board diagnosis of the catalytic converter is a challenging task, as it relies on indirect assessments of catalyst activity. Several methods have been proposed for catalyst diagnosis, presenting a varying degree of correlation between the quantities used as OBD indexes and the actual tailpipe emissions. This paper evaluates two methods, with the support of mathematical modeling; in the first one, which is commonly used by vehicle manufacturers, malfunction detection relies on the oxygen storage properties of the catalyst, while in the second, detection relies on the heat released by the chemical reactions in the catalyst. Both are found to be sufficient for the diagnosis of catalytic converters for current legislation requirements. However, the thermal method presents higher sensitivity to low levels of catalyst deactivation and could therefore be more suitable for diagnosis of future, ultra-low-emitting vehicles.