We study synchronization of nonlinear systems with robustness to disturbances that arise when measurements sent from the master system to the slave system are affected by quantization and time sampling. Viewing the synchronization problem as an observer design problem, we invoke a recently developed theory of nonlinear observers robust to output measurement disturbances and formulate a sufficient condition for robust synchronization. The approach is illustrated by a detailed analysis of the Pecora-Carroll synchronization scheme for the Lorenz system, for which an explicit bound on the synchronization error depending on the quantizer range and sampling period is derived.