77Se-NMR is used to characterise several chalcogen bonded complexes of derivatives of the organoselenium drug ebselen, exploring a range of electron demand. NMR titration experiments support the intuitive understanding that chalcogen bond donors bearing more electron withdrawing substituents give rise stronger chalcogen bonds. The chemical shift of the selenium nucleus is also shown to move upfield as it participates in a chalcogen bond. Solid-state NMR is used to explore chalcogen bonding in co-crystals. Due to the lack of molecular reorientation on the NMR timescale in the solid state, the shape of the chemical shift tensor can be determined using this technique. A range of co-crystals are shown to have extremely large chemical shift anisotropy, which suggests a strongly anisotropic electron density distribution around the selenium atom. A single crystal NMR experiment was conducted using one of the co-crystals, affording the absolute orientation of the chemical shift tensor within the crystal. This showed that the selenium nucleus is strongly shielded in the direction of the chalcogen bond, and strongly deshielded in the perpendicular direction, consistent with the presence of a second σ-hole which is not participating in a chalcogen bond.