The Jones matrix measured with an optical vector analyzer (OVA) is the result of a cascade of individual Jones matrices representing the input fiber path, device under test (DUT), and output fiber path. To extract the DUT matrix, compensation of the random polarization rotation on the Poincaré sphere caused by the input and output fiber is necessary. In this letter, we present a novel algorithm that factors out the Jones matrix of the fiber pigtails and enables the DUT matrix to be resolved in a convenient reference frame. A mathematical description of the algorithm is presented and the algorithm is verified by measuring a wave plate and a polarization converter. The efficacy of the algorithm is demonstrated through characterization of a microring resonator (MRR) including round-trip loss, ring-bus coupling coefficient, and group delay of each polarization beyond the magnitude response represented by Q -factor.