We report a study of proton spin relaxation of an Iridium N-heterocyclic carbene complex [Ir(COD)(IMes)Cl] complex (where COD=1,5-cyclooctadiene, Imes=1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene). This compound is a pre-catalyst of the most efficient complex allowing the signal amplification by reversible exchange (SABRE) effect, relevant for enhancing weak signals in nuclear magnetic resonance (NMR). An important feature of the study is a combination of relaxation measurements over a wide field range with high-resolution NMR detection. As a result, we are able to measure nuclear magnetic relaxation dispersion (NMRD) curves in the field range 0.1 mT-16.4 T (corresponding to the frequency range 4 kHz-700 MHz) for individual protons in the complex under study. This attractive possibility enables determination of the motional correlation times, τc, for the individual protons by analyzing the features in the NMRD curves (increase of the relaxation times) appearing at the magnetic fields where ωτc&-apcode;1 (here ω is the proton Larmor precession frequency at a given field strength). The following correlation times were determined: (1.3±0.1) ns for the protons of imidazol-2-ylidene, (0.96±0.1) ns for the ortho-protons of two phenyl moieties and (0.95±0.2) ns for the protons of methyl groups. Additionally, we report low-field features coming from "strong coupling" of the protons. One should note that such features must not be misinterpreted by associating them with motional features. From the low-field features we obtain consistent estimates for the proton spin-spin interactions. The analysis of motional correlation times is also of importance for interpretation of spin order transfer from parahydrogen to various substrates in transient organometallic complexes (termed the SABRE effect) at high magnetic field.