As an energy carrier and with respect to fossil fuels, hydrogen has advantages with regard to availability and environmental impact, though several technical and economical problems require solution before industrial application, particularly with respect to production and storage. Hydrogen can be stored as a highly compressed gas at up to 700 bar, cryogenically liquefied at -253 °C or in bound form. Liquid hydrogen storage raises questions principally regarding pressure build-up, pressure relief (boil-off) and filling. Numerical models of liquid tank systems of thermodynamic equilibrium will be presented and accompanied by simulations of pressure build-up. The simulation results are compared with measurements carried out on cryogenic containers at HyCentA, though the potential for improvement in the quality of measurements is apparent. The chilling of connecting pipes and containers, so critical to hydrogen wastage, is also simulated and compared with measurements. In combination, the numerical models presented are capable of supporting appropriate parameter optimisation with respect to pressure, temperature and fill level in the presence of pressure build-up, boil-off and chilling. However, installation complexity and boil-off gas losses need to be minimised if filling stations are to be competitive in the longer term.