To obtain homogeneously microwave cured epoxy-glass composite samples greater than the wavelength of radiation, physical considerations and mathematical calculations of the wave propagation in dielectric filled waveguides show that a single-mode travelling wave is required. According to this conclusion, a process is developed, using matched tapered transitions at air-material incoming and material-air outgoing interfaces, to reduce reflections and nonuniformities. Mould materials are selected with a permittivity less than that of the material to be cured. Experiments show that satisfactorily homogeneously cured samples can be obtained through this way.