Characterizing paramagnetic complexes in solids is an essential step toward understanding their molecular functions. However, methodologies to characterize chemical and electronic structures of paramagnetic systems at the molecular level have been notably limited, particularly for noncrystalline solids. We present an approach to obtain connectivities of chemical groups and metal-binding structures for unlabeled paramagnetic complexes by C-13 and H-1 high-resolution solid-state NMR (SSNMR) using very fast magic angle spinning (VFMAS, spinning speed >= 20 kHz). It is experimentally shown for unlabeled Cu(II)(Ala-Thr) that 2D C-13/H-1 correlation SSNMR under VFMAS provides the connectivity of chemical groups and assignments for the characterization of unlabeled paramagnetic systems in solids. We demonstrate that on the basis of the assignments provided by the VFMAS approach multiple C-13-metal distances can be simultaneously elucidated by a combination of measurements of C-13 anisotropic hyperfine shifts and C-13 T-1 relaxation due to hyperfine interactions for this peptide-Cu(II) complex. It is also shown that an analysis of H-1 anisotropic hyperfine shifts allows for the determination of electron-spin states in Fe(III)-chloroprotoporphyin-IX in solid states.