Currently, new concepts for power generation are discussed, as a response to combat global warming due to CO2 emissions stemming from the combustion of fossil fuels. These concepts include new, low-carbon fuels as well as centralized and decentralized solutions. Thus, a more diverse range of fuel supplies will be used, with (biogenic) low-caloric gases such as syngas and coke oven gas (COG) among them. Typical for theses low-caloric gases is the amount of hydrogen, with a share of 50% and even higher. However, hydrogen mixtures have a higher reactivity than natural gas (NG) mixtures, burned mostly in today's gas turbine combustors. Therefore, in the present work, a combined experimental and modeling study of nitrogen-enriched hydrogen–air mixtures, some of them with a share of methane, to be representative for COG, will be discussed focusing on laminar flame speed data as one of the major combustion properties. Measurements were performed in a burner test rig at ambient pressure and at a preheat temperature T0 of 373 K. Flames were stabilized at fuel–air ratios between about φ = 0.5–2.0 depending on the specific fuel–air mixture. This database was used for the validation of four chemical kinetic reaction models, including an in-house one, and by referring to hydrogen-enriched NG mixtures. The measured laminar flame speed data of nitrogen-enriched methane–hydrogen–air mixtures are much smaller than the ones of nitrogen-enriched hydrogen–air mixtures. The grade of agreement between measured and predicted data depends on the type of flames and the type of reaction model as well as of the fuel–air ratio: a good agreement was found in the fuel lean and slightly fuel-rich regime; a large underprediction of the measured data exists at very fuel-rich ratios (φ > 1.4). From the results of the present work, it is obvious that further investigations should focus on highly nitrogen-enriched methane–air mixtures, in particular for very high fuel–air ratio (φ > 1.4). This knowledge will contribute to a more efficient and a more reliable use of low-caloric gases for power generation.