In this paper the emphasis is on the optimization of synthetic inertial response of wind power plants (WPPs) for power systems with high wind power penetration levels, considering different wind speed operating conditions. The synthetic inertial response of wind power plants can play an important role in the resilience of future power systems with low inertia during large frequency disturbances. In order to investigate this role, a generic optimization methodology employing the genetic algorithm is proposed, taking into consideration the frequency nadir, second frequency dip, and time to reach the quasi-steady-state frequency. This optimization methodology comprehends the inertial response capability of WPPs and the frequency control dynamics of the power system. Accordingly, offline parameter tuning of synthetic inertial response is performed at the power system level with the proposed methodology. Based on the optimization results, the relevant aspects to be considered by transmission system operators and wind power plant developers in the process of designing and planning synthetic inertia are identified and analyzed. Additionally, sensitivity analyses are carried out to assess the impact of synthetic inertial response parameters on power system frequency control performance under different contingencies and wind power penetration levels.