The shipboard power system of an all-electric ship can be characterized as an isolated microgrid system. To achieve resilient, cost-effective and privacy-preserved operation of the shipboard power system, a novel energy management strategy is proposed in this paper. Currently, a master controller is required for energy management. However, such a centralized energy management strategy suffers from numerous disadvantages. Therefore, a modified nested energy management method is proposed to preserve privacy and run the microgrid system in a distributed manner for plug-and-play operation. Furthermore, the system resilience is enhanced against energy deficiency by reserving more in the energy storage system. This is achieved by a distributed algorithm, known as alternating direction method of multipliers (ADMM), to obtain the solution of an optimization problem with contradicting objectives. Simulation results are presented to demonstrate the benefits of proposed energy management system.