Full polarimetric radio interferometric calibration is performed by estimating 2 by 2 Jones matrices representing instrumental and propagation effects. The solutions obtained in this way differ from the true solutions by a 2 by 2 unitary matrix ambiguity. This ambiguity is common to all stations for which a solution is obtained but it is different for solutions obtained at different time and frequency intervals. Therefore, straightforward interpolation of solutions obtained at different time and frequency intervals is not possible. In this paper, we propose to use the theory of quotient manifolds for obtaining correct interpolants that are immune to unitary matrix ambiguities.