This work presents a new pilot plant continuous microwave dry-media reactor (CMDR) for industrial chemical applications. The CMDR consists of a 6 kW conveyor microwave oven with a subsequent hot air holding section. This microwave reactor has been designed for dry media or solvent-free reactions and can treat through-put in the range of 10-100 kg/h. The microwave heating behavior on the small scale is analyzed and the results are used to estimate the electromagnetic field requirements on the large scale. The temperature and the electric field distribution in the reactor are modeled and experimentally validated. In the second part of this study, a "waxy" esterification reaction was investigated with the CMDR. The reaction time needed for 95% yield was reduced by a factor of 20-30 compared to conventional industrial reactors. This was due to the more homogeneous heat transfer of microwaves, which allows a higher bulk temperature to be reached.