An NMR structure refinement method for the NMR crystallography of zeolites is presented and demonstrated to give an NMR-determined crystal structure for the zeolite Sigma-2 that is in very good agreement with the single-crystal X-ray diffraction structure. The Si coordinates of the zeolite framework were solved from Si-29 double-quantum NMR data obtained at a low magnetic field strength (7.0 T) and the Si and O coordinates were subsequently refined using the principal components of Si-29 chemical shift tensors experimentally measured at an ultrahigh-field (21.1 T) and calculated using ab initio quantum chemical methods.