This paper investigates the effectiveness of standard centrality metrics for interdependent networks (IDN) in identifying important nodes in preventing catastrophic failure propagation. To show the need for designing specialized centrality metrics for IDNs, we compare the performance of these metrics in an IDN under two different scenarios: i) the nodes with highest centrality of networks composing an IDN are selected separately and ii) the nodes with highest centrality of the entire IDN represented as one single network are calculated. To investigate the resiliency of an IDN, a threshold-based failure propagation model is used to simulate the evolution of failure propagation over time. The nodes with highest centrality are chosen and are assumed to be resistant w.r.t failure. Extensive simulation is conducted to compare the usefulness of standard metrics to stop or slow down the failure propagation in an IDN. Finally a new metric of centrality tailored for interdependent networks is proposed and evaluated. Also, useful guidelines on designing new metrics are presented.