The primary objective of this paper is to alleviate the over-frequency problem in low-inertia power systems through optimal allocation of a Battery Energy Storage System (BESS). With prolific integration of wind power, conventional fossil-fuel driven synchronous generators are being replaced in the generation fleet. Variable speed wind machines are connected to the grid via power electronics converters. As such, these machines usually do not participate in frequency regulation. During high wind penetration, a generation-rich zone of an interconnected power system may face significant over-frequency following the loss of interconnection. If the frequency goes above a certain threshold, an Over-Frequency Generator Shedding (OFGS) scheme is activated. This may cause considerable amount of generation cut in a low-inertia power system. To address this challenge, this paper develops a siting and sizing methodology of frequency-responsive BESS to simultaneously maintain frequency and voltage stabilities. As such, BESS is placed at the most voltage-sensitive bus, determined by an index called reactive power margin. Furthermore, an optimization model is formulated to determine the BESS size to avoid generation shedding. The proposed technique is applied to a low-inertia power system, which resembles the equivalent high-voltage transmission network of South Australia. The simulation results reveal that the developed methodology successfully mitigates the over-frequency phenomenon. In addition, the proposed technique is found to be more effective than its counterpart (i.e., without BESS) to enhance the frequency resilience of a low-inertia grid.