Recent studies of cholesterol-rich membrane microdomains, called caveolae, reveal that caveolae are reservoirs of recruitable sodium ion channels. Caveolar channels constitute a substantial and previously unrecognized source of sodium current in cardiac cells. In this paper we model for the first time caveolar sodium currents and their contributions to cardiac action potential morphology. We show that the beta-agonist-induced opening of caveolae may have substantial impacts on peak overshoot, maximum upstroke velocity, and ultimately conduction velocity. Additionally, we show that prolonged action potentials and the formation of potentially arrhythmogenic afterdepolarizations, can arise if caveolae open intermittently throughout the action potential. Our simulations suggest that there may exist routes to delayed repolarization, and the arrhythmias associated with such delays, that are independent of channelopathies.