We investigate the ferromagnetic resonance (FMR) response of microfabricated microwave resonators loaded with small Co16Pd84 alloy rectangles. A major increase in the FMR signal-to-noise ratio is achieved by employing the microwave-resonator structure. A FMR peak shift similar to that of Co16Pd84 continuous films is measured in the presence of hydrogen gas in the sample environment. We show that the very high sensitivity of the FMR signal of the Co16Pd84 alloy rectangle to hydrogen exposure can be used to measure relatively small hydrogen-concentration steps near 100% H2. Additionally, we also demonstrate that this structure can measure hydrogen over a concentration range from 3% to 100% H2 in N2. In time-dependent FMR measurements, we discover a temperature dependence of the FMR signal, which we relate to intrinsic temperature-dependent changes in saturation magnetization and the magnetic anisotropy of the Co-Pd alloy.