The present work focuses on the combustion performance of a premixed methane-air mixture with hydrogen and steam addition in micro-combustors with isothermal walls at 300 K. The reaction of the premixed flame under varying operating conditions is analyzed in terms of the centerline temperatures, flame temperatures, maximum heat of reaction in the vicinity of the reactive front, and the mass fraction of various species involved in the combustion process. The interactions between flame position, temperature, and species concentrations caused in the micro-combustor for 10% and 20% hydrogen addition ratios are studied using the ANSYS Fluent solver. The simulation results depict that hydrogen addition significantly escalates the reaction rate, flammability range, and flame stability, increasing the OH mole concentration and reducing the ignition time. An increase in the hydrogen addition ratio causes the flame position to gradually shift toward the combustor inlet, with the flame temperature increasing steadily by about 3.5% for every 10% hydrogen addition. However, this can be countered by adding steam to the incoming mixture, which helps to push the flame to its original location. The steam amount required to reinstate the flame to its original position corresponding to the two hydrogen percentages has been determined.