This paper focuses on the coordinated operation of multiple microgrids (MMG) connected via shared energy storage (SES) to realize energy interaction across microgrids. An MMG-SES operation optimization strategy taking into account the multiple utilization of hydrogen energy and green certificate-carbon trading is proposed. To increase the proportion of wind and other renewable energy consumption and achieve low-carbon system operation, a hydrogen model of multiple utilization and the GCT-CET (carbon emission trading-green certificate trading) mechanism are introduced. By quantifying the carbon emission reduction value of green certificates and allowing market players to offset carbon quotas with the emission reduction of green certificates, the synergy between the green certificate market and the carbon trading market is realized. On this basis, an MMG-SES cooperative operation model is constructed and equivalently transformed into two subproblems: minimizing cooperative cost and maximizing trading tariff, which are solved by the alternating direction method of multipliers (ADMM). Case study results show that the proposed model effectively reduces the operating costs of microgrid systems and shared energy storage power stations, enhances new energy consumption capacity, reduces carbon emissions, and realizes efficient energy use and low-carbon economic operation.