Olivine-type LiCoPO4 (LCP) is a high energy density lithium ion battery cathode material due to the high voltage of the Co2+/Co3+ redox reaction. However, it displays a significantly poorer electrochemical performance than its more widely investigated isostructural analogue LiFePO4 (LFP). The co-substituted LiFexCo1-xPO4 olivines combine many of the positive attributes of each end member compound and are promising next-generation cathode materials. Here, the fully lithiated x = 0, 0.25, 0.5, 0.75 and 1 samples are extensively studied using P-31 solid-state nuclear magnetic resonance (NMR). Practical approaches to broadband excitation and for the resolution of the isotropic resonances are described. First principles hybrid density functional calculations are performed on the Fermi contact shift (FCS) contributions of individual M-O-P pathways in the end members LFP and LCP and compared with the fitted values extracted from the LiFexCo1-xPO4 experimental data. Combining both data sets, the FCS for the range of local P environments expected in LiFexCo1-xPO4 have been calculated and used to assign the NMR spectra. Due to the additional unpaired electron in d(6) Fe2+ as compared with d(7) Co2+ (both high spin), LFP is expected to have larger Fermi contact shifts than LCP. However, two of the Co-O-P pathways in LCP give rise to noticeably larger shifts and the unexpected appearance of peaks outside the range delimited by the pure LFP and LCP P-31 shifts. This behaviour contrasts with that observed previously in LiFexMn1-xPO4, where all P-31 shifts lay within the LiMnPO4-LFP range. Although there are 24 distinct local P environments in LiFexCo1-xPO4, these group into seven resonances in the NMR spectra, due to significant overlap of the isotropic shifts. The local environments that give rise to the largest contributions to the spectral intensity are identified and used to simplify the assignment. This provides a tool for future studies of the electrochemically-cycled samples, which would otherwise be challenging to interpret.