The challenge of storing hydrogen at high volumetric and gravimetric density for automotive applications has prompted investigations into the potential of cryo-adsorption on the internal surface area of microporous organic polymers. A range of Polymers of Intrinsic Microporosity (PIMs) has been studied, the best PIM to date (a network-PIM incorporating a triptycene subunit) taking up 2.7% H2 by mass at 10 bar/77 K. HyperCrosslinked Polymers (HCPs) also show promising performance as H2 storage materials, particularly at pressures >10 bar. The N2 and H2 adsorption behaviour at 77 K of six PIMs and a HCP are compared. Surface areas based on Langmuir plots of H2 adsorption at high pressure are shown to provide a useful guide to hydrogen capacity, but Langmuir plots based on low pressure data underestimate the potential H2 uptake. The micropore distribution influences the form of the H2 isotherm, a higher concentration of ultramicropores (pore size <0.7 nm) being associated with enhanced low pressure adsorption.