This article addresses the numerical modeling of NOx emissions and lean blowoff (LBO) limits of confined and pressurized turbulent premixed flames stabilized with a low swirl burner. The study also evaluates existing numerical methods that can be used to predict exhaust pollutant emissions and reaction instability close to the LBO limit. One of the strategies presented in the article consists of establishing a chemical reactor network (CRN), which is a simplified model of the fluid dynamics and energy balance of the system coupled with a detailed reaction mechanism. Since the computing turnaround time for a CRN model is several orders of magnitude less than the simplest computational fluid dynamics (CFD) case, the parameters controlling the pollutant formation and stability of the system can be quickly assessed over the complete flammable range. The results show the value of a simple reactor network as a design tool that can be used to optimize emissions and LBO limits of combustion systems. The parametric analysis examines the most important variables that control the formation of pollutant species (pressure, recirculation of gases, heat losses, geometry variables, air to fuel ratio, and fuel composition). Experiments were carried out at a pressure of 304 kPa using two fuel compositions: natural gas and natural gas enriched with up to 90% hydrogen (by volume). The results obtained with the CRN for NOx and LBO are in good agreement with those observed experimentally and show that, for ultra-low NOx burners, the lowest NOx emissions are concomitant to the onset of instabilities associated with LBO. In sharp contrast, the CFD-based simulations of NOx fail to accurately predict the effect of the fuel composition on the LBO limit. Further analysis of the CRN results show that, at lean conditions and pressures above three atmospheres, NOx is formed primarily through the N2O pathway, regardless of the fuel composition. The CRN model indicates that adding hydrogen to natural gas promotes the production of NOx through the Zeldovich, NNH, and N2O routes while reducing formation via the prompt route. Understanding the relative contributions of each route provides a starting point from which to propose modifications to the system to reduce NOx emissions.