In this work, near-zero-index material boundary properties have been exploited to achieve new electromagnetic functionalities. The extraordinary guiding properties of a cylindrical dielectric rod waveguide surrounded by a thin epsilon-mu-near-zero shell is analyzed and discussed. A closed-form solution for the dispersion equation has been developed, able to model and design such properties at will. Analytical and numerical results will confirm that the use of near-zero cover materials leads to extraordinary properties in terms of field configurations, low attenuation, and bandwidth. The dielectric wire acts as an efficient "waveguide" with great potentials for advance nanocircuit and electronics.