In this paper, we present a novel auto-calibration scheme for the joint estimation of the two-dimensional (2-D) direction-of-arrival (DOA) and the mutual coupling matrix (MCM) for a signal measured using uniform circular arrays. The method employs an integrated wideband dictionary to mitigate the detrimental effects of the discretization of the continuous parameter space over the considered azimuth and elevation angles. This leads to a reduction of the computational complexity and obtaining of more accurate DOA estimates. Given the more reliable DOA estimates, the method also allows for the estimation of more accurate mutual coupling coefficients. The method utilizes an integrated dictionary in order to iteratively refine the active parameter space, thereby reducing the required computational complexity without reducing the overall performance. The complexity is further reduced by employing only the dominant subspace of the measured signal. Furthermore, the proposed method does not require a constraint on the prior knowledge of the number of nonzero coupling coefficients nor suffer from ambiguity problems. Moreover, a simple formulation for 2-D non-numerical integration is presented. Simulation results show the effectiveness of the proposed method.