The problem of near-field partially polarized electromagnetic source localization using an array of cross-dipoles, each of which consists of one x-axis dipole and one y-axis dipole, is addressed. The maximum likelihood (ML) algorithm for estimating the angle and range parameters is developed. This algorithm requires no search over the polarization parameters. We also show that the ML algorithm can be implemented by processing the x-axis dipole data and the y-axis dipole data separately. In addition, a subspace-based algorithm, which is based on the ideas of MUSIC and generalized ESPRIT, is presented. This algorithm decouples the two-dimensional (2D) search into two successive one-dimensional (1D) searches, where the angle and range parameters are estimated in succession. The deterministic Cramer-Rao bound (CRB), for the problem under consideration, is also derived. The performance of the subspace-based algorithm is evaluated and compared with that of the ML algorithm and the CRB.