The high-resolution 27Al and 31P NMR spectra of two as-synthesized forms of the microporous aluminophosphate AlPO-14 and the corresponding calcined-dehydrated form were assigned using both "first-principles" calculations of NMR parameters (GIPAW, as implemented in NMR-CASTEP) and a 27Al-31P heteronuclear correlation NMR experiment (MQ-J-HETCOR) that exploits 27Al multiple-quantum coherences and J couplings to identify Al-O-P linkages. NMR parameters calculated from published AlPO-14 crystal structures, which are derived from powder X-ray diffraction (XRD) data, are in poor agreement with experiment and it was necessary to optimize the structure geometry using energy minimization before satisfactory agreement was obtained. Comparison of simulated powder XRD patterns from the experimental and the energy-minimized structures shows that the changes in relative atomic positions in the optimized structure are relatively small and yield only minor adjustments in the Bragg peak intensities. These results indicate that a combination of NMR spectroscopy and first-principles calculation of NMR parameters may soon be considered a generally useful step in the refinement of the structures of microporous materials derived from powder diffraction data.