This paper presents a method for estimating the orientation of a directional sound source emitting a broadband acoustic signal being recorded by a microphone array, given source directivity, microphone positions with respect to the source and recordings of the call. Such a method has been tested to evaluate its precision in an ordinary laboratory environment, by placing a Polaroid transducer at several known positions and orientations and recording calls it emitted with a microphone array. Experiments discussed herein focus on accuracy in estimating the true transducer orientation for both an analytical directivity model and when directivity is provided by measurements. Results show that method estimates orientations very close to the true ones, and that analytical directivity is a good approximation of the measured one. We also point out the limits we must respect to make the method precise. The signal emitted by the source is broadband, like the signals many bats use while echolocating. Indeed, our intended final application of the method is to estimate the orientations a bat assumes while hunting over water.