This study identifies the type and size of the optimal shunt limiting impedance for superconducting fault current limiter (SFCL). Since the shunt impedance has been widely categorised to be either inductive or resistive element depending on the type of limiting impedance, the proposed design considerations will significantly affect the transient response and system stability. Therefore, the presented problem formulation optimises the design of SFCL by allowing the limiting shunt impedance to combine both resistive and inductive elements with an optimal ratio to tackle the security and stability challenges while functioning the SFCL. The optimisation framework is developed based on time-domain simulation and takes into account the transient stability indices to size the limiting components of SFCLs given that the main operational requirements such as fault current level and voltage limits are met. Non-dominated sorting genetic algorithm II is used to find the Pareto fronts for different types of SFCLs. The optimisation and time-domain simulation results demonstrate great enhancement in the performance of both SFCLs when the optimal ratio between the resistive and inductive elements is chosen for the shunt limiting impedance resulted in improving the transient response and system stability.