Marine lifting surfaces undergo flow-induced vibrations leading to shorter life cycles due to structural fatigue and reduced acoustic performances. As such, accurate understanding of the fluid-structure response of marine structures, as well as vibrations control and damping, are critical to many maritime applications. In particular, this work investigates the potential of the electromechanical coupling inherent to piezoelectric materials for passive vibration damping of hydrofoils under hydrodynamic flows. An aluminium flat plate equipped with piezoelectric patches connected to a resonant shunt is considered. The structure is first tested under hydrodynamic flows for various Reynolds numbers to investigate its flow-induced vibrations. This allows to determine the natural frequency of interest to test the control solution. Second, an experimental modal analysis is carried out to determine the open and short circuit natural frequencies in order to compute the piezoelectric coupling factor. Indeed, the latter is related to the expected performance of the passive vibration damping strategy. Third, the values for the resistive and inductive components of the RL-shunt are inferred from the coupling factor and the natural frequencies. Last, the control solution is tested in still air and water in open and short circuits configurations. Comparisons of these two configurations are realised and the resonant shunt performance for vibration reduction of hydrofoils is estimated.