This paper proposes an approach to estimate the required size of Energy Storage System (ESS) to emulate virtual inertia for a low inertia microgrid. The Distributed Energy Resources (DER) based microgrid system consists of Solar Photovoltaic (SPV), Wind Farm (WF) and Synchronous Machine (SM) based Diesel power generation unit feeding local loads. ESS based Virtual Synchronous Generator(VSG) considered in microgrid is operating in grid supporting mode [6] synchronised using PLL. ESS-VSG unit is utilised for compensating the lack of inertia in Power Electronics interfaced distributed generation boosting the resiliency of microgrid in unison with SM. The virtual inertia injection is achieved using swing equation based Virtual Synchronous Generator algorithm. The severe most contingency in addition with appropriate value of Virtual Inertia Hvsg and Damping Dvsg is selected to determine the ESS capacity for inertia injection such that overall frequency transient and steady state response is enhanced. ESS capacity is estimated considering ESS-VSG unit is only responsible for inertial and primary frequency response during the time of disturbances and does not participate in load sharing during steady state operation. © 2022 IEEE.