This work presents an adaptive control methodology that facilitates correct adaptation in the presence of actuator saturation constraints, model errors and initial condition errors. The central idea is to modify the reference trajectory on saturation, in such a way that the modified trajectory approximates the original reference closely, and can be tracked within saturation limits. Asymptotic stability of the tracking errors between the plant trajectories and the modified reference, and bounded learning of the adaptive parameters is guaranteed. Simulation results are presented for tracking of an attitude reorientation trajectory for a rigid spacecraft.