Most modern electromagnetic devices consist of dielectric and magnetic particulate composites. Predicting the effective electric permittivity and effective magnetic permeability of the envisioned composite is of great importance in validating the design for such applications. In this work, we propose a numerical method based on Yee's scheme and statistically generated representative volume element to estimate these effective electromagnetic properties for linear isotropic composites made with ellipsoidal particles. By considering particle geometry and composite microstructure precisely, it provides a more accurate tool for their design than available analytical bounds. Several numerical examples of composite microstructures are presented to demonstrate the capability of the proposed method. Comparison with analytical bounds and experimental results from literature is conducted to show validity.