An advanced low-NOx combustor is studied experimentally in the frame of the recent European Program EEFAE (Efficient and Environmentally Friendly Aero-Engine) for the CLEAN (Component vaLidator for Environmentally-friendly Aero-eNgine) demonstrator. The experimental measurements are compared with model predictions obtained using a 3-D computational fluid dynamics (CFD) proprietary code properly coupled with a numerical tool called Kinetic Post-Processor (KPP). One of the aims of this paper is also to describe a methodology for computing steady turbulent reacting flows in complex shape combustors: the thermo-fluid dynamics results of the CFD code are processed by the KPP with the use of detailed kinetics for predicting pollutant emissions, with special emphasis to nitrogen oxides. The comparisons between experimental measurements and model predictions indicate the current limitations of the procedure but also the possibilities of this powerful tool. From the kinetics point of view, the need for accurate high-pressure experimental data on NOx formation is also highlighted.