The N-15 principal values and orientations of the chemical shift tensors of beta-HMX are obtained by means of a FIREMAT experiment. A fitting routine using first-order perturbation theory to account for the residual dipolar coupling from neighboring N-14 nuclei, responsible for broadening and/or splitting of the N-15 resonances, was used to obtain the information from the experimental data. Intermolecular electrostatic interactions are incorporated into nitrogen chemical shielding calculations using several theoretical molecular models. The embedded ion method, a charge model, produced charge densities that improved the correlation between experimental chemical shifts and calculated chemical shieldings by 60% over single-molecule calculations, thus bringing the RMS within anticipated experimental error. The improvements made by the embedded ion method also provided the means to assign the nitrate resonances.