In this paper, we propose metrics and an evaluation method for survivability, which captures the extent of functionality retained by a system after a disruptive event. Our approach can be applied to a system with an arbitrary, but known, topology. We quantify survivability in terms of the extent and rate of degradation of a domain-specific figure-of-merit. The results are used in importance analysis to identify components most frequently involved in system-level failures, as well as components whose failure have the most severe consequences. As a case study, we have analyzed three smart grids, respectively based on the IEEE 14-, 30-, and 57-bus test systems. Using simulation-based fault injection, we evaluate their survivability in the presence of failures resulting from corrupted data, transmission line outages, and loss of power regulators. Two figures of merit were used, namely the customer service index and the average nominal voltage error. Our work provides means for quantifying and predicting the service degradation caused by failure of parts of a cyber-physical smart grid. It also enables efforts to fortify critical systems and mitigate their inevitable failures.