The catalytic partial oxidation (CPO) of methane with oxygen was studied at atmospheric pressure in a continuous-flow reactor containing a single Pt metal gauze. Experiments were performed at catalyst temperatures and residence times in the range of 950–1200 K and 0.02–0.2 ms, respectively. Heat-transport limitations are taken into account explicitly, by measuring the catalyst temperature directly by means of a surface thermocouple. The experimental results indicated that the conversions of methane and oxygen were determined by transport phenomena; however, the CO selectivity appeared to be influenced significantly by the kinetics of the catalytic reactions. Hydrogen was found only at temperatures above 1273 K. In order to be able to derive intrinsic kinetic information from the experimental data, a reactor model consisting of two rows of parallel flat plates in series was developed, taking into account the relevant transport phenomena. This flat-plate reactor model was validated by comparing the model results to 3D simulations of simultaneous heat and mass transfer in case of a simple surface reaction on the gauze catalyst. A series-parallel CPO reaction mechanism allowed simulation of the observed conversions and selectivities at different space-times. More detailed elementary-step reaction mechanisms can be developed, using both the experimental data and the flat-plate reactor model.