We present a drilling method that is based on the phenomenon of local hot spot generation by near-field microwave radiation. The microwave drill is implemented by a coaxial near-field radiator fed by a conventional microwave source. The near-field radiator induces the microwave energy into a small volume in the drilled material under its surface, and a hot spot evolves in a rapid thermal-runaway process. The center electrode of the coaxial radiator itself is then inserted into the softened material to form the hole. The method is applicable for drilling a variety of nonconductive materials. It does not require fast rotating parts, and its operation makes no dust or noise.