A computational experiment investigating the [superscript 1]H and [superscript 13]C nuclear magnetic resonance (NMR) chemical shifts of molecules with unpaired electrons has been developed and implemented. This experiment is appropriate for an upper-level undergraduate laboratory course in computational, physical, or inorganic chemistry. The chemical shift range for paramagnetic systems differs substantially from the well-known range of diamagnetic compounds. Students carried out density functional theory calculations of the chemical shifts of an organic radical and a related closed-shell system. This simple exercise illustrated that a single unpaired electron may result in dramatically different chemical shifts. Organometallic systems were also considered. The chemical shifts of the closed shell molecule ferrocene were compared to those of vanadocene and nickelocene, which afford three and two unpaired electrons, respectively. A natural bonding orbital (NBO) analysis was employed to study the electronic structure of NiCp[subscript 2].