The electromagnetic fields of charges moving along the boundary of a “wire metamaterial” perpendicularly to the wires are investigated. The metamaterial under consideration represents a volume-periodic structure of thin parallel wires located in a square lattice. This structure is described by an effective permittivity tensor and exhibits both spatial and frequency dispersion. It is shown that the charge generates nondivergent radiation, as in the case of an infinite metamaterial. However, unlike the infinite-metamaterial case, the radiation concentrates near a certain plane (not line) behind the charge, and it is asymmetric with respect to this plane. An algorithm for calculating the wave fields of finite-length bunches is developed, and some typical numerical results are given. They demonstrate that the structure under consideration can be applied to determine the size and form of such bunches. The stopping and deflection forces acting on the charge are also calculated.