Polynomial broadband beamforming designs enable an easy, smooth, and dynamic steering of the main beam. A number of design methods based on constrained optimization have been proposed recently which allow for the control of the robustness of these designs. Of course, the addition of robustness constraints reduces the number of degrees of freedom of the design. In this paper, we present a method to enhance the spatial selectivity of the robust polynomial beamformer design by exploiting the structure of symmetric arrays while still satisfying the robustness constraints. The effectiveness of this method is shown in design examples for symmetric linear and circular arrays.