Adaptive beamforming antennas capable of accommodating the growing number of wireless subscribers throughout the world has become an essential part of modern wireless systems. In this work, the beamforming of a conformal antenna on a changing conformal surface is studied by relating the varying position of each antenna element in the array to the weighting coefficients (i.e, array weights) required to give a desired antenna beam formation. In particular, the beamforming of a 1 x 4 array on a changing wedge- and cylindrical-shaped surface is studied using the projection method on a wavefront of a transmitted wave in a particular direction. To validate the theory, a 1 x 4 prototype antenna with individual voltage-controlled phase shifters and attenuators is used to implement the computed weights of each individual antenna element for measurements in an anechoic chamber. Overall agreement between theory, simulations and measurements is shown throughout the work. Furthermore, the effects of mutual coupling and changing conformal surfaces on the behavior of the beamforming pattern and array weights is investigated and summarized.