The relative humidity (RH) sensing behavior of a polymeric film was investigated by means of polymer coated surface acoustic wave (SAW) delay lines implemented on single crystal piezoelectric substrates, such as quartz and LiNbO3, and on thin piezoelectric polycrystalline films, such as ZnO and AlN, on Si and GaAs. The same SAW delay line configuration was implemented on each substrate and the obtained devices’ operating frequency was in the range of 105–156 MHz, depending on the type of the substrate, on its crystallographic orientation, and on the SAW propagation direction. The surface of each SAW device was covered by the same type RH sensitive film of the same thickness and the RH sensitivity of each polymer coated substrate, i.e., the SAW relative phase velocity shift per RH unit changes, was investigated in the 0%—80% RH range. The perturbational approach was used to relate the SAW sensor velocity response to the RH induced changes in the physical parameters of the sensitive polymer film: the incremental change in the mass density and shear modulus of the polymer film per unit RH change were estimated. The shift of the bare SAW delay lines operating frequency induced by the presence of the polymer film, at RH=0% and at T=-10 °C, allowed the experimental estimation of the mass sensitivity values of each substrate. These values were in good accordance with those reported in the literature and with those theoretically evaluated by exact numerical calculation. The shift of the bare SAW delay lines propagation loss induced by the polymer coating of the device surface, at RH=0% and at ambient temperature, allowed the experimental estimation of the elastic sensitivity of each substrate. These values were found in g- ood accordance with those available from the literature. The temperature coefficient of delay and the electromechanical coupling coefficient of the bare substrates were also estimated. The membrane sensitivity to ethanol, methanol and isopropylic alcohol was tested by means of a high-frequency (670 MHz) high-sensitivity Si/AlN resonator sensor.