The interpretation of nuclear spin relaxation data of biomolecules often requires the accurate knowledge of chemical shielding anisotropy (CSA) tensors, which significantly depend on the environment and on intramolecular dynamics. CSA tensors are studied in this work by density functional theory and by molecular dynamics simulations. It is demonstrated that density functional theory yields CSA tensors for N-15 nuclei in the side chain of crystalline asparagine and in the peptide bond of crystalline alanine-alanine dipeptide with an accuracy comparable to that of solid-state NMR. In these calculations, the molecular fragment containing the nucleus of interest is treated with an IGLO-II and IGLO-III basis set while neighboring fragments exhibiting close contacts are represented by a DZVP set. In addition, electrostatic effects are taken into account by explicit partial point charges. The dynamical averaging of CSA tensors is investigated by applying density functional theory to snapshots of a molecular dynamics trajectory of the protein ubiquitin. The fluctuation properties of the N-15 CSA tensors of two glutamine side chains are assessed. Computed auto- and cross-correlated relaxation parameters using these CSA tensors are found to be in good agreement with the experiment. Local charges and close contacts can have a significant effect on N-15 CSA tensors and have to be taken into account when transferring CSA parameters from model compounds to proteins.