Widening of the operating potential window is a straightforward route towards increasing the specific energy of electrochemical capacitors. Usually, the assessment of the viable potential range is committed to thermodynamic considerations over the electrolyte potential window and experimental probing of the electrochemical stability of both electrolyte and electrode materials through cyclic voltammetry. However, while the former approach is too conservative, the latter is prone to failure. In the present work, we consider quantitative approaches for monitoring the influence of the potential window on the dissipative behaviour of aqueous electrochemical capacitors. For proving the concept underlying this work, we analyse as a case study an asymmetric cell with a reduced graphene oxide / MnO2 positive electrode and a carbon nanotube based negative electrode, as well as nominally symmetric cells assembled with either electrode. We apply and compare different procedures to define the safe potential window of these systems: the usual potential window opening technique, applied either to single electrodes or packed cells; and not conventional methods, based on the analysis of either the energy efficiency or the cell impedance as a function of the cell-2-potential. Precisely, we analyse the trend of the energy efficiency, derived from galvanostatic charge / discharge experiments, and that of the real component of the cell impedance vs. the potential window, to discriminate the onset of irreversible processes leading to dissipative losses. The viability of the proposed methods and the reliability of the attendant criteria are finally checked in the light of the results of cycling performance of the asymmetric cell.