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One of complementary value propositions of microgrids is to improve power system resiliency via local supply of loads and curtailment reduction. This subject is investigated in this paper by proposing a resiliency-oriented microgrid optimal scheduling model. The proposed model aims at minimizing the microgrid load curtailment by efficiently scheduling available resources when supply of power from the main grid is interrupted for an extended period of time. The problem is decomposed to normal operation and resilient operation problems. The normal operation problem solution, i.e., unit commitment states, energy storage schedules, and adjustable loads schedules, is employed in the resilient operation problem to examine microgrid capability in supplying local loads during main grid supply interruption. The schedule is revised via resiliency cuts if a zero mismatch is not obtained. Prevailing operational uncertainties in load, non-dispatchable generation, and the main grid supply interruption time and duration are considered and captured using a robust optimization method. The final solution, which is obtained in an iterative manner, is economically optimal, guarantees robustness against prevailing operational uncertainties, and supports a quick islanding with minimum consumer inconvenience and load curtailment. Numerical simulations demonstrate the effectiveness of the proposed resiliency-oriented microgrid optimal scheduling model applied to a test microgrid.