A robust stability assessment approach is presented to efficiently estimate eigenvalues in microgrids in the presence of bounded uncertainties. Through this method, all possible locations of eigenvalues can be directly obtained, which makes repeatedly eigenvalue calculation unnecessary when dealing with uncertainties. More importantly, a quasi-diagonalization technique is established to reduce the conservativeness of the Geršgorin theory. Extensive tests show that the new method enables highly efficient analysis on impact levels of disturbances and offers a useful tool for droop coefficients design which facilitates microgrids stable operation. Besides, test results show that the Geršgorin theory based approach can be effectively combined with other methods to obtain more accurate solutions. These salient features make the new method a powerful tool for planning, operating, and designing future microgrids.