NMR is a powerful tool for obtaining information on the structural characterization and dynamics of proteins, and nucleic acids, and their complexes. The complexity of the spectra is such that elucidation through computational simulation is a much desired thing. However, the size of most structures of interest is such that they remain out of reach of accurate quantum chemical techniques. Fragmentation methods have been shown to be a viable means of reducing the cost of ab initio calculations to enable the prediction of molecular properties of large systems to chemical accuracy. We look at the systematic molecular fragmentation by annihilation method for a model peptide system and show that this procedure reproduces the shielding constants of a full calculation at only a fraction of the cost. Discussion of the considerations needed in applying this method is discussed and comparison made with the results of the similar fragment molecular orbital and ONIOM methods.