Accurate and robust thermochemical models are required to identify future low-NOx technologies that can meet the increasingly stringent emissions regulations in the gas turbine industry. These mechanisms are generally optimized and validated for specific ranges of operating conditions, which result in an abundance of models offering accurate nominal solutions over different parameter ranges. At atmospheric conditions, and for methane combustion, a relatively good agreement between models and experiments is currently observed. At engine-relevant pressures, however, a large variability in predictions is obtained as the models are often used outside their validation region. The high levels of uncertainty found in chemical kinetic rates enable such discrepancies between models, even as the reactions are within recommended rate values. The current work investigates the effect of such kinetic uncertainties in NO predictions by propagating the uncertainties of 30 reactions, that are both uncertain and important to NO formation, through the combustion model at engine-relevant pressures. Understanding the uncertainty sources in model predictions and their effect on emissions at these pressures is key in developing accurate thermochemical models to design future combustion chambers with any confidence. Lean adiabatic, freely-propagating, laminar flames are therefore chosen to study the effect of parametric kinetic uncertainties. A non-intrusive, level 2, nested sparse-grid approach is used to obtain accurate surrogate models to quantify NO prediction intervals at various pressures. The forward analysis is carried up to 32 atm to quantify the uncertainty in emissions predictions to pressures relevant to the gas turbine community, which reveals that the NO prediction uncertainty decreases with pressure. After performing a Reaction Pathway Analysis, this reduction is attributed to the decreasing contribution of the prompt-NO pathway to total emissions, as the peak CH concentration and the CH layer thickness decrease with pressure. In the studied lean condition, the contribution of the pressure-dependent N2O production route increases rapidly up to 10 atm before stabilizing towards engine-relevant pressures. The uncertain prediction ranges provide insight into the accuracy and precision of simulations at high pressures and warrant further research to constrain the uncertainty limits of kinetic rates to capture NO concentrations with confidence in early design phases.