The genetically encoded amino acid selenocysteine and its dimeric form, selenocystine, are both utilized by nature. They are found in active sites of selenoproteins, enzymes that facilitate a diverse range of reactions, including the detoxification of reactive oxygen species and regulation of redox pathways. Due to selenocysteine and selenocystines specialized biological roles, it is of interest to examine their 77Se NMR properties and how those can in turn be employed to study biological systems. We report the solid-state 77Se NMR measurements of the L-selenocystine chemical shift tensor, which provides the first experimental chemical shift tensor information on selenocysteine-containing systems. Quantum chemical calculations of l-selenocystine models were performed to help understand various structural effects on 77Se l-selenocystines chemical shift tensor. The effects of protonation state, protein environment, and substituent of selenium-bonded carbon on the isotropic chemical shift were found to be in a range of ca. 10-20 ppm. However, the conformational effect was found to be much larger, spanning ca. 600 ppm for the C-Se-Se-C dihedral angle range of -180 degrees to +180 degrees. Our calculations show that around the minimum energy structure with a C-Se-Se-C dihedral angle of ca. -90 degrees, the energy costs to alter the dihedral angle in the range from -120 degrees to -60 degrees are within only 2.5 kcal/mol. This makes it possible to realize these conformations in a protein or crystal environment. 77Se NMR was found to be a sensitive probe to such changes and has an isotropic chemical shift range of 272 +/- 30 ppm for this energetically favorable conformation range. The energy-minimized structures exhibited calculated isotropic shifts that lay within 3-9% of those reported in previous solution NMR studies. The experimental solid-state NMR isotropic chemical shift is near the lower bound of this calculated range for these readily accessible conformations. These results suggest that the dihedral information may be deduced for a protein with appropriate structural models. These first-time experimental and theoretical results will facilitate future NMR studies of selenium-containing compounds and proteins.