An increasing penetration of renewable generation has led to reduced levels of rotational inertia and damping in the power network. The consequences are higher vulnerability to disturbances and deterioration of the dynamic response of the system. To overcome these challenges, novel converter control schemes that provide virtual inertia and damping have been introduced, which raises the question of optimal distribution of such devices throughout the network. This paper presents a comprehensive framework for performance-based allocation of virtual inertia and damping to the converter-interfaced generators in a detailed low-inertia system. This is achieved through an iterative, eigensensitivity-based optimization algorithm that determines the optimal controller gains while simultaneously preserving small-signal stability and ensuring that the damping ratio and frequency response after disturbances are kept within acceptable limits. Two conceptually different problem formulations are presented and validated on a modified version of the well known Kundur’s two-area system as well as a larger 59-bus South-East Australian network.