A novel method to determine the fiber-matrix interfacial properties of ceramic matrix composites is proposed and evaluated; where micro-pillar samples containing inclined fiber/matrix interfaces were prepared from a SiC fiber-reinforced SiC matrix composites and then compression-tested using the nano-indentation technique. This new test method employs a simple geometry and mitigates the uncertainties associated with complex stress state in the conventional single-filament push-out method or tensile unloading-reloading hysteresis loop analysis method for the determination of interfacial properties. Based on the test results using samples with different interface orientations, the interfacial debond shear strength and the internal friction coefficient are explicitly determined and compared with values obtained by other test methods. SEM observation showed that micro compression caused an adhesive type of debonding between the fiber and the pyrolytic carbon interface. The results suggest that the debonding/failure behavior of the micro-pillars followed the Coulomb fracture criterion. The determined interfacial debond shear strength is similar to 100 MPa, which appears to be smaller than that determined from fiber push-out test for similar composite systems. The difference can be explained by the effect of normal stress (clamping stress) on the apparent interfacial debond shear strength.