In summary, we have developed a systematic bottom-up method for coarse-graining molecular simulations models using anisotropic coarse-grained (CG) particles, called the anisotropic force-matching coarse-graining (AFM-CG) method, which generalizes the multiscale coarse-graining (MS-CG) method for parametrizing CG models with isotropic (spherical) particles via force and torque matching. We have derived rigorous conditions for the CG masses, moments of inertia, forces and torques that must satisfy to ensure thermodynamic consistency in the canonical equilibrium ensemble between the anisotropic CG model and the fine-grained (FG) model from which it is derived, given the interaction potential between FG particles and a definition CG position and orientation coordinates in terms of FG coordinates. As in the MS-CG method for isotropic CG particles, the force on an anisotropic CG particle in the AFM-CG method must equal the average total force acting on the FG particles mapped onto the CG particle for equivalent FG and CG configurations.