Properties of circular coaxial waveguide antennas terminated in a plane conductor are analyzed where in the most general case the center conductor is of infinite extent. Solutions for mutual admittance and radiated fields are detailed for all asymmetric modes. An asymptotic solution is also derived for the far-zone fields. We describe results for TE11 mode excitation of coaxial waveguides where 1) outside the aperture the conductor is absent, and 2) the center conductor extends to infinity. These antennas are of practical interest as feeds for reflectors. Experimental results are described for several examples and excellent agreement with theory is shown. Comparison of the two cases shows that in 1) there is always an optimum frequency for good pattern symmetry and low cross polarization. The mismatch in case 2) is less than in 1) but pattern symmetry is poor if the ratio of inner to outer conductor radius is greater than about 0.2. Further, in 2) mutual coupling to adjacent annular rings is stronger and the principal plane radiation patterns has widely spaced phase centers.