We apply the local many-particle method of the Effective Hamiltonian of Crystal Field (EHCF) to analyze the magnetic ground state and the low-energy excitation spectra of the transition-metal carbodiimides MNCN with M = Fe-Ni. Experimentally, these materials represent a uniform group of (high-spin) antiferromagnetic, optically transparent, colored insula tors with absorption lines in the visible spectrum. These findings are fully supported by the EHCF numerical modeling. In all three cases, we arrive at high-spin ground states in agreement with the results of previous magnetic measurements as well as the presence of the d-d intrashell transitions for the visible absorption spectra. Remarkably enough, the EHCF approach resolves the controversial case of FeNCN which was earlier predicted to be metallic by density-functional theory even when including explicit electronic correlation (GGA+U). We also address the ground state and the low-energy excitation spectra of the transition-metal hydrocyanamides of the general formula M(NCNH)(2) with M = Fe-Ni, another uniform group of optically transparent colored insulators. EHCF also arrives at high-spin ground states and visible d-d intrashell transitions.