A method for conversion of greenhouse gases comprises: introducing a flow of a dehumidified gaseous source of carbon dioxide into a reaction vessel; introducing a flow of a dehumidified gaseous source of methane into the reaction vessel; and irradiating catalytic material in the reaction vessel with microwave energy. The irradiated catalytic material is heated and catalyzes an endothermic reaction of carbon dioxide and methane that produces hydrogen and carbon monoxide. At least a portion of heat required to maintain a temperature within the reaction vessel is supplied by the microwave energy. A mixture that includes carbon monoxide and hydrogen can undergo catalyzed reactions producing multiple-carbon reaction products in a lower-temperature portion of the reaction vessel.