Modern fault-resilient microgrids (MGs) require the operation of healthy phases during unbalanced short-circuits to improve the system reliability. This study proposes a differential power based selective phase tripping scheme for MGs consisting of synchronous and inverter-interfaced distributed generators (DGs). First, the differential power is computed using the line-end superimposed voltage and current signals. Subsequently, to make the scheme threshold-free, a power coefficient index is derived and used for identifying faulted phases in an MG. The protection scheme is tested on a standard MG operating in either grid-connected or islanding mode, which is simulated using PSCAD/EMTDC. The efficacy of the scheme is also assessed on the OPAL-RT manufactured real-time digital simulation (RTDS) platform. Further, the performance of the proposed protection scheme is compared with a few existing methods. The results show that the selective tripping of faulted phases in MGs can be achieved quickly and securely using the proposed scheme.