The direct homogeneous partial oxidation of methane to methanol is investigated through modeling and a limited set of experiments. The experiments are conducted in a laminar flow quartz reactor at 100 bar and 598-763 K under undiluted conditions. The modeling is performed with a detailed chemical kinetic model, previously validated against a range of high-pressure data on oxidation of CO/H-2 and small hydrocarbons. Modeling predictions compare well also with the experimental data obtained in the present study. On the basis of the chemical kinetic modeling, the effect of the main process parameters is discussed and the process is optimized, using a numerical global optimization methodology based on interval analysis. The experimental data, as well as the optimization results, indicate yields of methanol in the upper range of those reported in literature. However, the values are well below the commercial target.