Closed bipolar cells (cBPCs) can offer valuable platforms for the development of electrochemical sensors. On the other hand, such systems are more intricate to model and interpret than conventional systems with a single polarizable interface, with the applied potential "splitting" into two polarized interfaces where two coupled charge transfers take place concomitantly. As a result, the voltammetry of cBPCs shows peculiarities that can be misleading if analyzed under the framework of classic electrochemical cells. In this work, rigorous mathematical solutions are deduced for the cyclic voltammetry (CV) of cBPCs, including the current-potential response, the interfacial potentials, and the interfacial redox concentrations. With such theoretical tools, a comprehensive view of the behavior of cBPCs can be gained, and adequate diagnosis criteria are established on the basis of the shape, magnitude, and position of the CV signal as a function of the scan rate and of the experimental conditions in the anodic and cathodic compartments.