High penetration of wind power into power systems is likely to cause difficulties in maintaining system frequency, as in contrast to conventional synchronous generators, variable speed wind turbines (VSWTs) do not directly contribute to system inertia. To overcome this issue, it has been proposed to emulate inertia by VSWTs by extracting the kinetic energy of the turbine rotor. However, proper designing of the inertia emulating controller is essential for the optimal use of the energy potential and safe operation of the wind turbine. Some of the common controller concepts used for inertia emulation have inherent weaknesses, limiting the frequency support provided by VSWTs. This paper highlights these design considerations by simulating the inertial responses provided by a typical controller. To overcome the identified issues, a new controller design is proposed. Its capability to provide an improved frequency response while reducing the adverse impacts on the turbine rotor is demonstrated.