We consider electromagnetic scattering by a spherical volume sparsely and randomly populated by spherical particles of equal size and optical properties. The far-field scattering matrix of the entire volume is computed using an exact method and an approximate method. The former is a direct computer solver of the Maxwell equations called the superposition T-matrix method (STMM). The latter is a solver based on numerical Monte Carlo integration of the ladder and cyclical diagrams appearing in the microphysical theory of radiative transfer and coherent backscattering (RT–CB). The quantitative agreement between the STMM and RT–CB computations provides verification of the RT–CB theory. Prominent backscattering features exhibited by the STMM data cannot be reproduced by keeping only the ladder diagrams of RT. Our results strongly support the CB explanation of opposition brightness and polarization phenomena observed for a class of atmosphereless solar-system objects. Further research is necessary to determine the range of quantitative applicability of the RT–CB theory to densely packed particulate media.