The theoretical background and computational implementation of the multi-scale coarsegraining (MS-CG) method that uses force matching to parametrize interactions between isotropic CG particles has been introduced previously. The method provides a rigorous statistical-mechanical framework for determining the interactions between CG particles so that the equilibrium phase-space distribution of the CG system is consistent with that of the atomically detailed FG system from which it is derived. Here we generalize the MS-CG method to CG models consisting of anisotropic particles, in which the system configuration is defined not only by particle positions, as in the case of isotropic (spherical) particles, but also by particle orientations. Consider a FG system comprising n spherical particles (atoms), with particle positions and momenta r n ≡ (r 1 , ..., r n ) and p n ≡ (p 1 , ..., p n ), respectively, for which the potential energy as a function of FG particle coordinates is u(r n ). This FG system is to be mapped onto a CG representation comprising N anisotropic sites, where N < n, whose configuration is defined by both the CG particle positions R N ≡ (R 1 , ..., R N ) and their orientations Ω N ≡ (Ω 1 , ..., Ω N ). The conjugate momenta to these CG position and angular coordinates are the linear momenta P N ≡ (P 1 , ..., P N ) and angular momenta L N ≡ (L 1 , ..., L N ), respectively.