Magnetic anisotropy in cyanide-bridged single-molecule magnets (SMMs) with Fe-III-CN-M-II (M = Cu, Ni) exchange-coupled pairs was analyzed using a density functional theory (DFT)-based ligand field model. A pronounced magnetic anisotropy due to exchange was found for linear Fe-III-CN-M-II units with fourfold symmetry. This results from spin-orbit coupling of the [Fe-III(CN)(6)](3-) unit and was found to be enhanced by a tetragonal field, leading to a E-2(g) ground state for Fe-III. In contrast, a trigonal field (e.g., due to tau(2g) Jahn-Teller angular distortions) led to a reduction of the magnetic anisotropy. A large enhancement of the anisotropy was found for the Fe-III-CN-Ni-II exchange pair if anisotropic exchange combined with a negative zero-field splitting energy of the S = 1 ground state of Ni-II in tetragonally compressed octahedra, while cancellation of the two anisotropic contributions was predicted for tetragonal elongations. A recently developed DFT approach to Jahn-Teller activity in low-spin hexacyanometalates was used to address the influence of dynamic Jahn-Teller coupling on the magnetic anisotropy. Spin Hamiltonian parameters derived for linear Fe-M subunits were combined using a vector-coupling scheme to yield the spin Hamiltonian for the entire spin cluster. The magnetic properties, of published oligonuclear transition-metal complexes with ferromagnetic ground states are discussed qualitatively, and predictive concepts for a systematic search of cyanide-based SMM materials are presented.