This paper presents the design and optimization of high quality (Q) factor inductors using Micro Electro-Mechanical Systems (mEMs) technology for 10GHz to 20GHz frequency band. Two inductors have been designed with square and circular topologies. Inductors are designed on Silicon-on-Sapphire (SOS) because of its advantages including high resistivity and low parasitic capacitance. The effects of various parameters such as the width of metal traces (W), the thickness of the metal (T) and the air gap (AG) on the Q-factor are thoroughly investigated. Results indicate that the optimization of the geometrical parameters has minimized the resistive, capacitive and inductive losses of the inductor.