The integration of Energy Storage Systems (ESSs) in contemporary applications highly depends on the performance of these devices. Supplying high power for a reasonable period of time is one of their main targets in several applications like backup systems and transport technologies. For this purpose, Lithium-Ion Capacitors (LICs) would demonstrate better suitability than conventional ESSs for applications requiring a small installation space and a long lifetime. They are known for their energy density greater than that of Supercapacitors (SCs) and their power density greater than that of Lithium-Ion Batteries (LIBs). This paper explains the electrochemical processes that interfere in the storage of energy inside a LIC. The analysis of these phenomena was the tool for assessing the nonlinear capacitance evolution of the LIC with respect to its voltage. Several measurement techniques in the frequency and time domains were elaborated and compared in order to assess this nonlinear behavior of the LIC. Some of the measurement protocols contained constant voltage phases that had a significant effect on the variation of the capacitance. The novelty of this study concerns the introduction of a new measurement protocol that takes into account the particular characteristics of LICs. Their unique behavior is explained for the first time based on a physicochemical analysis.