This paper details the experimental and numerical analysis of a combustion process for atmospheric swirl burners using methane with added ammonia as fuel. The research was carried out for lean methane–air mixtures, which were doped with ammonia up to 5% and preheated up to 473 K. A flow with internal recirculation was induced by burners with different outflow angles from swirling blades, 30° and 50°, where tested equivalence ratio was 0.71. The NO and CO distribution profiles on specified axial positions of the combustor and the overall emission levels at the combustor outlet were measured and compared to a modelled outcome. The highest values of the NO emissions were collected for 5% NH3 and 50° (1950 ppmv), while a reduction to 1585 ppmv was observed at 30°. The doubling of the firing rates from 15 kW up to 30 kW did not have any great influence on the overall emissions. The emission trend lines were not proportional to the raising share of the ammonia in the fuel. 3D numerical tests and a kinetic study with a reactor network showed that the NO outlet concentration for swirl flame depended on the recirculation ratio, residence time, wall temperature, and the mechanism used. Those parameters need to be carefully defined in order to get highly accurate NO predictions—both for 3D simulations and simplified reactor-based models.