Damping induced by vertically sloshing liquids at large amplitudes is of interest in the understanding of the dynamic response of aircraft wings containing fuel. This work presents the experimental investigation of sloshinginduced damping in two small rectangular tanks (L = 100 mm, h = 37.5 mm and 50 mm) under vertical excitation at various frequencies (3.3 to 10.3 Hz) and amplitudes (up to 1.57 tank heights). The focus is placed on large amplitudes that lead to violent vertical interactions between the liquid and the tank and the nonlinear damping effects they cause. The sloshing-induced dissipative energy in dimensional form shows a deviation from linearity with increasing amplitude of excitation, which is attributed to force-displacement hysteresis sub-cycle formations. When increasing the frequency of excitation, it is shown that the damping increases initially, and then remains constant. These findings are confirmed by a kinematics-based ballistic-harmonic model. Optical flow and a new technique based on pixel intensity standard deviation are employed in correlation with an analysis of the hysteresis cycles in order to offer insight into the sloshing force variation within one liquid cycle of oscillation.