Synchronization is a phenomenon of the collective behavior of coupled oscillators and involves the detailed interplay of the intrinsic frequencies of the oscillators, the underlying topological features of their interaction network, and external perturbations. In this work we investigate, in the strong coupling regime, the response of a system to external perturbations of its natural frequencies and network modifications. Our investigation relies on two performance measures (one for phases and the other for frequencies) and a spectral perturbation analysis. Given strongly localized perturbations in time, corresponding to the dominant eigenmode of the weighted Laplacian matrix of the network, we present a sufficient condition for the maximization of the system's stability, along with analytical results for the effects of structural perturbations on the system's response. A number of simulations are conducted to illustrate the theory presented.