The novel application of microwave directional couplers to develop angular-displacement microwave sensors is reported. The proposed sensor approach employs as stator a branch-line-type coupler arranged in transversal mode by loading its direct and coupled ports with two distinct-length open-ended stubs. Thus, by taking the isolated port of the coupler as the stator output node, a bandpass filtering transfer function with transmission zeros (TZs) is created. Then, a rotor made up of an angularly-moveable open-ended stub is attached to a curved section of the longest loading stub of the stator through physical contact, so that their interconnection point varies with the angular-displacement of the rotor. In this manner, the sensor transfer function is altered with the stub rotation through TZ reallocation, angular-displacement sensing capabilities are achieved. The theoretical operational foundations of the conceived branch-line-coupler-based microwave angular-displacement sensor, which features single/multi-band sensing properties in terms of inter-TZ spacing and stop band attenuation levels, along with design examples and curves are provided. The extrapolation of this sensor principle to other classes of power-distribution circuits, such as the rat-race-type directional coupler, is also demonstrated. Finally, for experimental-validation purposes, two 920 MHz microstrip prototypes of the conceived branch-line-coupler-based angular-displacement microwave-sensor approach are built and measured.