The need to reduce greenhouse gas (GHG) emissions while still providing energy for a growing world population is a major current challenge, in which decarbonizing domestic cooking plays an important role. Blending hydrogen derived from renewable energy sources into the natural gas network is being promoted alongside electrification. However, switching to hydrogen–natural gas blends can affect combustion processes in residential and commercial appliances, both in terms of performance and safety, since methane and hydrogen differ in their physical and chemical properties. While mixtures with low hydrogen content have safety measures and risks comparable to those of natural gas, the consequences become more pronounced with higher levels of hydrogen. Furthermore, different combustion technologies perform differently where supplied with hydrogen/natural gas blends. The present study focuses on investigating the influence of hydrogen–natural gas blends with up to 20% hydrogen on domestic ovens, both with and without thermostatic control. Heat input and maintenance consumption measurements, based on EN 30 standards, demonstrated that the addition of hydrogen results in a slight reduction of the heat input, despite the small increase in flow rate due to the lower Wobbe Index (WI) of hydrogen/natural gas blend. In the experiments, a negligible impact on safety issues and a reduction in CO exhaust emissions was also observed. Additional tests based on SASO 167 showed an insignificant influence of the hydrogen/natural gas blends on temperature distribution in the ovens chamber. The results confirm the safety and suitability of the tested oven models when using hydrogen/natural gas blends with up to 20% hydrogen. It is considered that the obtained results will encourage the use of these blends, thus contributing to the decarbonization of domestic cooking.