The concept of resilience-i.e., the ability of a unified structure to absorb shocks-is of high relevance in the context of network modelling and analysis, mainly when referred to finance. This paper starts from this premise, and deals with the resilience of a financial interbanking system. At this aim, we firstly introduce a new measure of the resilience of a network, by taking into full consideration the influence of the topology of the network and the weights of its links in the shocks propagation; then, we build one financial network model related to the quarterly-based interbanking sector, whose weights are calibrated on high quality empirical data; lastly, we compute the resilience measure of the considered networks. A discussion of the results is provided, by considering both finance and network theory perspectives.