An accurate analysis of planar aperture sectoral horns is presented. It is based on a simple adaptation of the mode matching technique, which allows for the inclusion of the aperture effect in the analysis without resorting to the conventional integral equations formulation. This technique provides accurate results, which are confronted with experiments and then used in a parametric study of the sectoral horns, aimed at achieving a constant beamwidth over an octave bandwidth or more. It is concluded that for the narrow E- plane aperture horn this objective is hard to attain, hence a different, convex aperture antenna is used. Experimental design of this configuration leads to the desired performance of a nearly constant beamwidth over more than an octave.