The development of NMR crystallography methods requires a reliable database of chemical shifts measured for systems with known crystal structure. We measured and assigned carbon and hydrogen chemical shifts of twenty solid natural amino acids of known polymorphic structure, meticulously determined using powder X-ray diffraction. We then correlated the experimental data with DFT-calculated isotropic shieldings. The small size of the unit cell of most amino acids allowed for advanced computations using various families of DFT functionals, including generalized gradient approximation (GGA), meta-GGA and hybrid DFT functionals. We tested several combinations of functionals for geometry optimizations and NMR calculations. For carbon shieldings, the widely used GGA functional PBE performed very well, although an improvement could be achieved by adding shielding corrections calculated for isolated molecules using a hybrid functional. For hydrogen nuclei, we observed the best performance for NMR calculations carried out with structures optimized at the hybrid DFT level. The high fidelity of the calculations made it possible to assign additional signals that could not be assigned based on experiments alone, for example signals of two non-equivalent molecules in the unit cell of some of the amino acids.