Considering piezoelectric damping, a resonant shunt can lead to a significant vibration reduction when tuned to the mechanical mode to control. However, limits appear when looking at practical applications in a low frequency range: the required inductance is often too high to be satisfied with standard passive components. Moreover, even if the inductor is eventually available, the internal resistance of the component generally exceeds the value which is required for a shunt optimization. Suitable inductors can be designed for applications requiring high inductance and low resistance values. Indeed, the permeance of a magnetic circuit can be significantly increased by the use of closed cores made of high permeability materials. In this paper, three designs are described and compared: an inductor from standard series and two handmade inductors involving a ferrite core and a nanocrystalline toroid. The components are successively integrated into a piezoelectric shunt dedicated to the vibration control of a cantilever beam. Depending on the frequency of the target mechanical mode to control, the benefits and the limits of the different inductors are observed. It is shown that custom designs can definitely extend to lower frequency the application of the passive resonant shunt strategy.