The natural frequency of a rubber-damped torsional vibration absorber (TVA) depends on the excitation amplitudes and frequencies in a highly nonlinear manner. This is due to nonlinear shear properties of the rubber ring. In this study, the nonlinear static and dynamic shear characteristics of a rubber ring, and the natural frequency of a nonlinear TVA are experimentally characterized firstly. Since a rubber ring employed in a rubber-damped TVA is usually in the compression state, its static and dynamic shear properties depend upon the compression ratio and dimensions apart from the chemical ingredients in a highly complex manner. The prediction of the natural frequency of a rubber-ring TVA thus poses considerable complexities. In this study, a special fixture is designed and fabricated for characterizing shear properties of a rubber ring subject to different compression ratios. The shear properties are subsequently characterized using different constitutive models, and a methodology for identifying the model parameters is presented considering the measured properties. Second, a methodology for estimating the natural frequency of the TVA is proposed, and the effectiveness of the proposed method is demonstrated through comparisons of the estimated natural frequency with the measured values. The results of the study suggest that the model using fractional derivatives to characterize nonlinear shear properties of a rubber ring can be effectively used to obtain accurate estimation of natural frequency of a nonlinear TVA over a wide range of excitations. The natural frequency of a TVA can thus be accurately estimated before prototyping using the experimental and modeling methods developed in this paper.