Although matching effects in superconducting anti-dot arrays have been studied extensively through magneto-resistance oscillations, these investigations have been restricted to a very narrow temperature window close to the superconducting transition. Here, we report a “two coil” mutual inductance technique, which allows the study of this phenomenon deep in the superconducting state, through a direct measurement of the magnetic field variation of the shielding response. We demonstrate how this technique can be used to resolve outstanding issues on the origin of matching effects in superconducting thin films with periodic array of holes grown on anodized alumina membranes.