Two wedges, one made of negative-permittivity material (primary) and another of an ordinary dielectric (auxiliary/secondary), are posed nose-to-nose to form a “bowtie” configuration. This shape is very common and convenient for a number of real-world devices and constructions such as electron microscopes, optical superlenses, and nanotips. In all these structures, the efficient operation and functionality get strongly assisted by the increased electromagnetic power concentration in the vicinity of the edge. Such a field enhancement is attempted with proper choice of the characteristics of the dielectric wedge to increase the field intensity over the cross section of the metamaterial one. A slowly varying field assumption is adopted to formulate approximate solutions to similar structures (sharp and rounded corners). A quality factor has been defined based on the power carried by the supported modal waves, if they are excited by a suitable electric source, in the presence and in the absence of the auxiliary wedge. This quantity expresses the intensity enhancement that could be achieved and is represented in graphs with respect to the dielectric wedge parameters. The characteristics of the secondary component that lead to a maximization of the electric power into the primary one are identified and explained. In particular, periodic variations of the angular extent of the secondary wedge are observed, and the number of maxima is increased with the dielectric permittivity of the constituent material.