We present a phase-amplitude reduction framework for networked dynamical systems collectively exhibiting stable limit-cycle oscillations. The framework takes into account both the dynamics along the limit cycle and deviations from the limit cycle, described by the phase variable and the amplitude variables, respectively. Phase-amplitude reduction allows us to analyze the dynamics of weakly interacting limit-cycling networks including synchronization. As an example, we optimize the phase locking of a network of FitzHugh-Nagumo elements by a periodic signal. By deriving the optimal injection signal and applying feedback control, we can stabilize the collective oscillations of the network without altering the phase dynamics and realize fast synchronization.