A new technique is proposed for the solution of pairing problem which is observed when fast algorithms are used for two-dimensional (2-D) direction-of-arrival (DOA) estimation. Proposed method is integrated with array interpolation for efficient use of antenna elements. Two virtual arrays are generated which are positioned accordingly with respect to the real array. ESPRIT algorithm is used by employing both the real and virtual arrays. The eigenvalues of the rotational transformation matrix have the angle information at both magnitude and phase which allows the estimation of azimuth and elevation angles by using closed-form expressions. This idea is used to obtain the paired interpolated ESPRIT algorithm which can be applied for arbitrary arrays when there is no mutual coupling. When there is mutual coupling, two approaches are proposed in order to obtain 2-D paired DOA estimates. These blind methods can be applied for the array geometries which have mutual coupling matrices with a Toeplitz structure. The first approach finds the 2-D paired DOA angles without estimating the mutual coupling coefficients. The second approach estimates the coupling coefficients and iteratively improves both the coupling coefficients and the DOA estimates. It is shown that the proposed techniques solve the pairing problem for uniform circular arrays and effectively estimate the DOA angles in case of unknown mutual coupling.