The damping ratio values of three different Danube sands were measured in the Resonant Column-Torsional Simple Shear device (RC-TOSS). The distinctive configuration of the RC-TOSS device employed in this investigation enabled the performance of both tests using a single sample. This research estimates and compares the damping ratio values measured with three distinct methods (two of which are in the RC test): The Free Vibration Decay (FVD), the Steady-State Vibration (SSV) methods, and the method of calculating the damping ratio from the hysteretic loops generated in the TOSS test. Both dense and loose samples were tested up to a peak-to-peak amplitude shear strain of 1%. The device provides measurements over a wide range of shear strain amplitudes. The results support the employment of the SSV methods at low strains (below 0.005%), while the FVD method gives a better estimate at higher strains (above 0.03%). The two methods and the TOSS results are in agreement with each other between 0.005% and 0.03%. The effect of the number of cycles on the damping ratio was investigated where a significant decrease was observed in the damping ratio with an increasing number of cycles. A parameter is introduced to describe the rate of this decrease, which should be considered during the structural design to reduce maintenance and life-cycle costs and enhance sustainability.