The textural characterization of a series of carbon molecular sieves (CMS) prepared from different polymer precursors has been investigated using N-2 adsorption at 77 K and CO2 adsorption at 273 K, together with immersion calorimetry into liquids of different molecular dimensions. Experimental results show that the carbon molecular sieves cover a wide range of porosity, front pure microporous CMS (pore diameter below 0.56 nm) to CMS combining larger micropores (above 0.7 nm) together with a certain proportion of mesoporosity. H-2 adsorption measurements on these CMS at cryogenic temperature (77 K) and ambient pressure (0.1 MPa) show that the hydrogen adsorption capacity exhibits a linear correlation with the volume of narrow micropores (V-n). Furthermore, these results confirm experimentally the necessity of a tailored micropore size in order to achieve an optimum packing density of the adsorbed hydrogen molecules (micropore size around 0.6 nm).