A theoretical analysis of the temperature-dependent P-31 NMR signals for the ambient pressure vanadyl pyrophosphate AP-(VO)(2)P2O7 and the oxovanadium hemihydrate hydrogenophosphate VO(HPO4).0.5H(2)O phases is reported. The ab initio calculation of the magnetic exchange parameters and the hyperfine constants gives access to an original ab initio simulation of NMR spectra. Such a strategy allows one to clarify the crystallographic nature of the different experimentally studied phases. For the vanadyl pyrophosphate ambient pressure structure, our simulations strongly support the presence of a monoclinic phase. Based on this assumption, hyperfine constants are extracted from the fit of the experimental data. These values are directly compared to the ab initio ones.