Understanding magnetorheology in saturating fields is crucial for success in high torque applications. In this paper we use numerical computations, analytical developments, and experimental data (using a double-gap magnetocell) to study the saturation behavior of model magnetorheological fluids for different particle loadings. Numerical calculations demonstrate a nonlinear dependence of both shear and normal stresses with particle concentration in contrast with analytical predictions. These predictions are in very good agreement with numerical calculations at low volume fractions when the interchain interactions can be safely neglected. Numerical calculations for the (yield) shear stress overestimate experimental data for small and medium concentrations. However, a reasonably good qualitative agreement is found for the larger particle loadings. Normal stresses are extraordinarily sensitive to the particular microstructure; experiments suggest sample dilatation in good agreement with simulations in lattices with a body-centered basis.