We introduce a measurement method that enables to measure the penetration depth($lambda$) of superconductor films by using a short-ended parallel plate sapphire resonator. Variations in the $lambda$ of $MgB_2$ films could be measured down to the lowest temperature using a sapphire resonator with a $YBa_2Cu_3O_{7-x}$ film at the bottom. A model equation of $lambda=lambda_0[1-(T/T_c)^{ au}]^{-1/2}$ for $MgB_2$ films appeared to describe the observed variations of the resonant frequency of the sapphire resonator with temperature, with $lambda_0,; au$, and $T_C$ used as the fitting parameters.