Humidified gas turbines using steam generated from excess heat feature increased cycle efficiencies. Injecting the steam into the combustor reduces NOx emissions, flame temperatures and burning velocities, promising a clean and stable combustion of highly reactive fuels, such as hydrogen or hydrogen-methane blends. This study presents laminar burning velocities for methane, and hydrogen-enriched methane (10 mol% and 50 mol%) at steam contents up to 30% of the air mass flow. Experiments were conducted on prismatic Bunsen flames stabilized on a slot-burner employing OH planar laser-induced fluorescence for determining the flame front areas. The experimental burning velocities agree well with results from one dimensional simulations using the GRI 3.0 mechanism. Burning velocities are increased with hydrogen enrichment, and reduce non-linearly with ascending steam molar fractions, showing the potential of steam dilution for a stable combustion of these fuels over a wide flammability range.