Skyrmions are found to be promising for next-generation energy-efficient spintronic applications. Moreover, ultrafast skyrmion dynamics in gigahertz-band offer an excellent opportunity to exploit such topologically protected nanostructures in high-frequency applications. Here, we present a systematic investigation of the microwave properties of the skyrmions in concentric and eccentric ring structures using micromagnetic simulations. Two gyrotropic modes with clockwise and counterclockwise gyration are observed in skyrmion when excited by an in-plane microwave field. The high-frequency response is found to be enhanced by 3.5 GHz by using a small bias field of 40 mT. The skyrmion dynamics are found to be extremely sensitive to the edge repulsions and a remarkably large frequency shift of 2 GHz of the skyrmion resonance modes is observed by simply varying the position of a skyrmion in an eccentric ring structure. The results are substantiated by directly correlating the observations with inertial mass associated with a skyrmion calculated analytically. The results provide an additional functionality of the skyrmions based on their tunable microwave properties which may have potential implications in the field of miniaturized reconfigurable microwave devices. © 1965-2012 IEEE.