Ab initio and density functional theory (DFT) calculations of nuclear magnetic resonance shielding tensors in benzene–methane and two isomers of the benzene dimer are reported, with the aim of probing the changes in shielding induced by the formation of supramolecular complexes from isolated molecules. It is shown that the changes in shielding (and hence of chemical shift) for hydrogen nuclei are broadly in line with expectations from “shielding cones” based on aromatic ring current, but that changes for carbon nuclei are rather more subtle. More detailed analysis indicates that the change in isotropic shielding results from much larger changes in individual components of the shielding tensor and in diamagnetic/paramagnetic shielding contributions. Benchmark data were obtained using Møller–Plesset 2nd order perturbation theory with a medium-sized basis set, but it is shown that Hartree–Fock and most density functional theory methods reproduce all essential changes in shielding, and do so in a reasonably basis set independent fashion. The chosen method is then applied to a DNA–intercalator complex.