The force-matching method has been applied to parameterise an empirical potential model for water-water and water-hydrogen intermolecular interactions for use in clathrate-hydrate simulations containing hydrogen guest molecules. The underlying reference simulations constituted ab initio molecular dynamics (AIMD) of clathrate hydrates with various occupations of hydrogen-molecule guests. It is shown that the resultant model is able to reproduce AIMD-derived free-energy curves for the movement of a tagged hydrogen molecule between the water cages that make up the clathrate, thus giving us confidence in the model. Furthermore, with the aid of an umbrella-sampling algorithm, we calculate barrier heights for the force-matched model, yielding the free-energy barrier for a tagged molecule to move between cages. The barrier heights are reasonably large, being on the order of 30 kJ/mol, and are consistent with our previous studies with empirical models [C. J. Burnham and N. J. English, J. Phys. Chem. C 120, 16561 (2016) and C. J. Burnham et al., Phys. Chem. Chem. Phys. 19, 717 (2017)]. Our results are in opposition to the literature, which claims that this system may have very low barrier heights. We also compare results to that using the more ad hoc empirical model of Alavi et al. [J. Chem. Phys. 123, 024507 (2005)] and find that this model does very well when judged against the force-matched and ab initio simulation data.