The geochemical and petrophysical complexity of source-rock reservoirs in liquids-rich unconventional (LRU) plays necessitates the implementation of a more expansive analytical protocol for initial play assessment. In this study, original samples from selected source-rock reservoirs in the USA and the UK were analyzed by 22 MHz nuclear magnetic resonance (HF-NMR) T1-T2 mapping, followed by hydrous pyrolysis, and a modified Rock-Eval pyrolysis method (multi-heating step method-MHS). The above methods were complemented by organic petrography under reflected white and UV light excitation of the original and pyrolyzed samples. The analytical protocol presented attempts to better qualify and quantify different petroleum fractions (mobile, heavy hydrocarbons, viscous, solid bitumen), thus provide valuable and refined information about producibility of target intervals during appraisal. Results show how the hydrocarbon fractions interpreted from peak locations and intensities on NMR T1-T2 maps are in good agreement with those from MHS pyrolysis in terms of hydrocarbon mobility/producibility. Results from HP (Hydrous Pyrolysis) experiments show that an exception to this general agreement between NMR and MHS estimates occurs for the Kimmeridge Blackstone Clay samples, where MHS shows an increase of >90% in producible hydrocarbon yields vs. minimal to no presence of mobile hydrocarbons in NMR T1-T2 maps. This study clarifies the role of pore structure and networks in these discrepancies of producible oil estimates when comparing programmed pyrolysis to NMR-based techniques. This novel, multi-step and multidisciplinary approach provides a more advanced screening protocol for identifying zones of higher oil-in-place (OIP) and predicting fluid mobility prior to drilling or completions.