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Microgrids are a feasible path to deploy smart grids, an intelligent and highly automated power system. Their operation demands a dedicated communication infrastructure to manage, control and monitor the intermittent sources of energy and loads. Therefore, smart devices will be connected to support the growth of grid smartness increasing the dependency on communication networks, which consumes a high amount of power. In an energy-limited scenario, one of the main issues is to enhance the power supply time. Therefore, this paper proposes a hybrid methodology for microgrid energy management, integrated with a communication infrastructure to improve and to optimize islanded microgrid operation at maximum energy efficiency. The hybrid methodology applies some control management rules, such as intentional load shedding, priority load management, and communication energy saving. These energy saving rules establish a trade-off between increasing microgrid energy availability and communication system reliability. To achieve a compromised solution, a continuous time Markov chain model describes the impact of energy saving policies into system reliability. The proposed methodology is simulated and tested with the help of the modified IEEE 34 node test-system. [ABSTRACT FROM AUTHOR]