Renewable energy sources (RESs) possess different fault signatures as compared to the traditional synchronous generators, thus introducing new challenges for microgrid protection. Among these challenges is phase selection, which is a prerequisite for selective phase tripping (SPT). This paper analyzes the root causes behind the failure of current-angle-based phase selection methods (PSMs) used by commercial relays in microgrids with inverter-interfaced RESs (IIRESs). Besides, the operation of the recently-developed voltage-angle-based PSM is investigated to unveil its points of strength and weakness. Then, adaptive zoning for the current-angle-based PSM is proposed to cope with the unconventional IIRES fault current signatures and enable precise SPT. As a result, microgrid reliability and resiliency during faults are enhanced. The proposed PSM depends on local measurements to update the PSM zones online by estimating the angles between the sequence impedances behind a relay. Comprehensive time-domain simulations verify the effectiveness of the proposed PSM at various fault resistances, fault locations, and microgrid topologies.