It is generally accepted that combustion of hydrogen and natural gas mixtures will become more prevalent in the near future, to allow for a further penetration of renewables in the European power generation system. The current work aims at the demonstration of the advantages of steam dilution, when highly reactive combustible mixtures are used in a swirl-stabilized combustor. To this end, high-pressure experiments have been conducted with a generic swirl-stabilized combustor featuring axial air injection to increase flashback safety. The experiments have been conducted with two fuel mixtures, at various pressure levels up to 9 bar and at four levels of steam dilution up to 25% steam-to-air mass flow ratio. Natural gas has been used as a reference fuel, whereas a mixture of natural gas and hydrogen (10% hydrogen by mass) represented an upper limit of hydrogen concentration in a natural gas network with hydrogen enrichment. The results of the emissions measurements are presented along with a reactor network model. The latter is applied as a means to qualitatively understand the chemical processes responsible for the observed emissions and their trends with increasing pressure and steam injection.