The time-dependent dynamics of the charge and discharge of photo-supercapacitors (PSC), devices which combine a supercapacitor with a solar cell, are investigated using a semi-analytical model. For a given PSC, it is found that the maximum Energy Conversion and Storage Efficiency (ECSE) is a direct function of the Power Conversion Efficiency (PCE) and Fill Factor (FF) of the solar cell. The capacitance, series and shunt resistances of the supercapacitor affect the time constants of the PSC and the value of the maximum ECSE. To experimentally measure the maximum value of ECSE with at most 2 charge-discharge cycles, a simple experimental procedure is proposed, which consists in comparing the power flowing through the supercapacitor and the energy already stored in it. The theoretical results are validated with experiments on a PSC made from an organic solar cell and a commercial supercapacitor.