With high penetration of renewable energy sources (RESs) in modern power systems, system frequency becomes more prone to fluctuation as RESs do not naturally have inertial properties. A conventional energy storage system (ESS) based on a battery has been used to tackle the shortage in system inertia but has low and short-term power support during the disturbance. To address the issues, this paper proposes a new synthetic inertia control (SIC) design with a superconducting magnetic energy storage (SMES) system to mimic the necessary inertia power and damping properties in a short time and thereby regulate the microgrid (µG) frequency during disturbances. In addition, system frequency deviation is reduced by employing the proportional-integral (PI) controller with the proposed SIC system. The efficacy of the proposed SIC system is validated by comparison with the conventional ESS and SMES systems without using the PI controller, under various load/renewable perturbations, nonlinearities, and uncertainties. The simulation results highlight that the proposed system with SMES can efficiently manage several disturbances and high system uncertainty compared to the conventional ESS and SMES systems, without using the PI controller.