We utilize quartz crystal resonators operating at multiple resonant harmonics to measure the high-frequency rheological properties of materials with a broad range of viscoelastic properties. The technique is demonstrated with poly(t-butyl acrylate) films in the vicinity of the calorimetrically determined glass transition and with rubbery polyisoprene films. The technique is a noncontact technique that can be used to quantify the temperature or time-dependent viscoelastic response in homogeneous films with thicknesses in the micrometer range. This work complements the ability of the resonators to quantify the viscoelastic behavior of viscoelastic polymer solutions and simple Newtonian liquids. For each material we obtain the density shear modulus product and the viscoelastic phase angle at frequencies of 5 and 15 MHz. A standardized analysis protocol is described that enables this information to be obtained reliably and accurately. The polyisoprene data are found to be in good agreement with measurements obtained by dynamic mechanical analysis using extrapolated temperature shift factors.