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The National Public Safety Telecommunications Council (NPSTC) has defined resiliency as the ability of a network to withstand the loss of assets and to recover quickly from such losses. How to measure the resiliency of a base station deployment is an important consideration for network planners and operators. In this paper, we propose a resiliency measurement method in conjunction with a performance metric such as coverage or supported throughput, where we define the resiliency as the maximum number of sites that can fail before the metric falls below a minimum acceptable threshold. Because the number of combinations of failures increases exponentially with respect to the number of sites in a given deployment, we introduce an algorithm that generates estimates of the lowest, highest, and average values of the metric for a given failure count while examining a subset of the possible failure combinations. We use an example deployment to demonstrate how the resiliency metric can be used to identify sites that have a disproportionate impact on performance; the network planner can harden these sites or, for a future deployment, adjust the site placement to reduce the effect of the high-impact sites.