Electromagnetic (EM) wave emission from the intrinsic Josephson junction stacks (IJJ’s) covered with a thin dielectric medium is numerically investigated, using the multi-scale simulation method developed in our previous paper. It is shown that the power of emitted EM waves is considerably increased in the IJJ’s with a dielectric cover. The emission from the n=2 resonance mode is greatly enhanced. The enhancement is caused by the excitation of a solitonic mode.