A two-step numerical concept (NOx post-processor) was developed at the Chair of Thermal Processing Technology to predict NOx emissions from non-premixed combustion accurately. The model was investigated with industrial burners and furnaces and was found to be computationally expensive. However, the post-processor had a faster computation time than the detailed chemistry approaches such as PaSR or EDC. In this thesis, the numerical model was investigated with three different optimisation strategies to reduce the computational effort further. The post-processor was improved with the open-source CFD tool OpenFOAM and investigated with measurement data from Sandia National Laboratories with the Flame D experiment. The available reaction rate calculation method was modified and analysed. A new strategy was proposed for initializing the values of the NOx post-processor with the Zeldovich mechanism. A mesh refinement technique was tested with the existing numerical model. Out of the three studied optimisation techniques, two techniques were found suitable for enhancing the performance of the post-processor by reducing the computation time. The accuracy of the post-processor remained unchanged through the implemented optimisation strategies. Two case studies were performed with industrial burners using the developed model. A Low-NOx burner was enhanced by reducing NOx emissions further by analysing the influence of the mass flow of primary to secondary air. The enhanced burner geometry was investigated with hydrogen-enriched natural gas. Another case study on an industrial staged burner was performed on a testing chamber and investigated the influence of hydrogen-enriched natural gas with ambient and preheated air. Both case studies were performed such that the energetic efficiency of the burners remains unchanged with different fuel mixtures consisting of hydrogen and natural gas. The influence of hydrogen-enriched natural gas on combustion and emission characteristics was analysed.