Combining quantum-chemical calculations and ultrahigh-field NMR measurements of Si-29 chemical shielding (CS) tensors has provided a powerful approach for probing the fine details of zeolite crystal structures. In previous work, the quantum-chemical calculations have been performed on 'molecular fragments' extracted from the zeolite crystal structure using Hartree-Fock methods (as implemented in Gaussian). Using recently acquired ultrahigh-field Si-29 NMR data for the pure silica zeolite ITQ-4, we report the results of calculations using recently developed quantum-chemical calculation methods for periodic crystalline solids (as implemented in CAmbridge Serial Total Energy Package (CASTEP) and compare these calculations to those calculated with Gaussian. Furthermore, in the context of NMR crystallography of zeolites, we report the completion of the NMR crystallography of the zeolite ITQ-4, which was previously solved from NMR data. We compare three options for the 'refinement' of zeolite crystal structures from 'NMR-solved' structures: (i) a simple target-distance based geometry optimization, (ii) refinement of atomic coordinates in which the differences between experimental and calculated Si-29 CS tensors are minimized, and (iii) refinement of atomic coordinates to minimize the total energy of the lattice using CASTEP quantum-chemical calculations. All three refinement approaches give structures that are in remarkably good agreement with the single-crystal X-ray diffraction structure of ITQ-4. Copyright (C) 2010 John Wiley & Sons, Ltd.