Laminar burning velocities and flammability limits of premixed methane/air flames in the presence of various inert gases including helium, argon, nitrogen and carbon dioxide were investigated by combined use of microgravity experiments and computations. The experiments used a short-drop free-fall laboratory facility that can eliminate the effect of buoyancy on flames and therefore enable accurate measurements of burning velocities, especially the near-limit values. Burning velocities were measured for outwardly propagating spherical CH4/air flames with varying concentrations of He, Ar, N2 and CO2. Flame behavior was also computed using the steady, one-dimensional laminar premixed flame code PREMIX. Results showed the capability of the diluents to reduce flame speed increases in the order He < Ar < N2 < CO2, due to their increased specific heat and decreased transport rates. The measured burning velocities are generally in good agreement with computations. Flammability limits were determined experimentally by finding the limiting concentration of diluents for which combustion can be initiated and propagated throughout the combustion chamber. It was found the limiting concentration for helium is lower than that for argon, indicating helium might be more effective near the limit. The Ar, N2 and CO2 mixtures at extinction correspond to low burning velocities, 2-3 cm/s. The helium mixture at extinction, however, corresponds to large burning velocity, about 18 cm/s. This behavior may be due to the high diffusivity of helium that causes rapid increase of the minimum ignition energy.