A new method for the design of antenna array feeding networks has been proposed in this work. In particular, the considered feeding networks are based on the Rotman lens. By knowing the maximum errors on the fabrication tolerances, the arithmetic of intervals and interval analysis (IA) are used for determining the lower and upper bounds of the antenna feeding network parameters of interest. Representative and preliminary numerical results are reported to show the potentialities of the proposed method. An experimental X-band Rotman lens prototype has been designed, fabricated, and assessed. The obtained results are quite good.