In this paper we propose strategies to increase the robustness of a communication network which depends on the proper functioning of an electricity network. The strategies involve selecting nodes of the communication network and removing their dependency on the electricity network. Compared to existing literature on this topic, such as Schneider et al. [1], we use a more realistic model of the electricity network by taking the essential characteristics of the power flow into account, instead of considering purely the topological structure. The effect of the flow-based cascading failures originating from the electrical grid, on the communication network is studied, where the coupling between those networks plays an important role. We have computed the performance of our proposed selection strategies by averaging over many configurations of communication networks, which are modelled both as scale-free networks and as Erdös-Rényi random graphs, applied to an electricity network formed by the IEEE 118 bus test system. We show that a hybrid strategy, based on the degree of the communication nodes and the failure probabilities of the electricity nodes, give a significant improvement over a random selection strategy, as well as over other strategies we proposed. Our method is also tested on a real-world interdependent network: the high voltage electricity grid in Italy coupled with a communication network, inspired by the Italy blackout in 2003.