A significant part of the light oil reserves in Russia is concentrated in low-permeable reservoirs, such as the Domanik Formation, Upper Devonian shales in the European part of Russia. Standard laboratory methods for estimating pore space structure and fluid saturation are often not applicable or not accurate in studying unconventional rocks. The presence of hydrocarbons with a high content of highly viscous components, including kerogen, and pores of nanometer size dramatically reduces the effectiveness of the conventional approaches in core analysis. This paper presents the results of an intensive study of Domanik organic-rich deposits by NMR relaxometry, Rock-Eval pyrolysis method, and lithological characterization (thin sections). More than 30 cylindrical core samples underwent a four-stage NMR complex consisting of T2 relaxation tests, two-dimensional T1-T2 maps for fluids identification, and saturation profile determination. Additionally, data on total organic carbon (TOC), obtained by the Rock-Eval method on a HAWK RW instrument (Wildcat Technologies) and results of lithological typing on thin sections using a polarization microscope (Axio Imager A2m, Carl Zeiss) were used for collection characterization. NMR tests were conducted on a low-field 2 MHz relaxometer unit (Geospec 2, Oxford Instruments). Series of NMR measurements were repeated for core samples in different states of saturation. The standard methodology of core samples preparation was also significantly changed in saturation conditions (pressure and duration) and extraction procedure (solvents combination). The suggested multi-stage procedure for analysis of low-permeable core samples with NMR profiling enables the quantitative and qualitative assessment of rock saturation with different fluids. An experimental study has shown that the suggested NMR methodology in conjunction with Rock-Eval pyrolysis method is appropriate for the study of carbonate rocks with a high content of organic microporous components, partially saturated with bitumen and viscous hydrocarbon fractions. Results include data on the structure of pores in samples, initial oil and water saturation, which can be used for predicting the most promising spots in the unconventional reservoir.