Microwave chemistry applications have been investigated for more than three decades. Contrary to common cavity-based microwave applicators, the traveling-wave microwave reactor has the potential to enable the process scale-up, a better coupling of microwave energy with microwave-susceptible catalysts, and consequently highly uniform microwave heating. In this work, the engineering challenges entailed with the design of a traveling-wave microwave waveguide are explained and appropriate solutions developed. A new traveling-wave microwave reactor with a coaxial waveguide structure is presented. Simulation results show that there is no standing wave generated along the structure. Furthermore, in order to keep the impedance matching and minimize the microwave reflections while the reactor is loaded with catalyst samples, new reactor's loading patterns are introduced. Simulation results showed that for the proposed method, microwave-susceptible catalytic fixed-bed could interact more efficiently with microwave energy and produce a uniform heating profile.