Recently, ultrathin localized spoof surface plasmon (LSSP) resonators are found to have intrinsic defects of relatively low quality factors (Q-factors) because of unavoidable material and radiation losses. In this paper, multilayer structures of planar-circular-grating resonators and their magnetic-coupling schemes are proposed to achieve effective excitation of high-Q LSSPs modes. By adopting the multilayer structures with air between the layers, the power dissipation effected by both material and radiation losses is significantly suppressed. Experimental results show that the Q-factors could reach more than 200 and the excitation efficiencies could reach more than 90%. Numerical simulations show the distribution of the electromagnetic field and illustrate the principle of magnetic coupling. Besides, the Q-factors of resonators with different structural parameters were measured and analyzed. This study aims to provide some inspirations on planar gyro-devices and to improve the performance of existing applications, such as sensors and filters.