We develop a methodology to evaluate the potential of microgrids to increase the resilience of critical infrastructure (CI) networks, and mitigate the impact of catastrophic failure in disaster situations. The methodology uses an optimization model to strategically locate microgrids and a network robustness analysis to determine the benefits of the new reinforced network. The location of microgrids seeks to ensure that a community's most important facilities have adequate power to provide services in the event of power grid failure. The analysis of network robustness evaluates the reinforced network in the event of the failure of increasingly larger sections of the network. The methodology was used to evaluate the installation of microgrids on ciciCIs in Puerto Rico, where the 2017 hurricane season caused catastrophic grid failure. The research team conducted data collection and fieldwork research in Puerto Rico, including interviews with disaster responders and CI managers. Prior to the installation of microgrids, small disruptions could completely cripple the power distribution system. In fact, our numerical experiments show that the destruction of 30% of the network in Puerto Rico was sufficient to result in a complete blackout. On the other hand, strategically adding microgrids to 30% of critical infrastructure can ensure functionality of the system even when 80% of the nodes in a power distribution network have been destroyed. These results show the potential benefits of strengthening the power grid with microgrids in relation to the robustness and resilience of CIs.