When accounting for polarization effects in radar and communications systems, it is often necessary to transform descriptions of the polarization state of an antenna or the polarization response of a target between local (or body-centered) and global coordinate frames. Such transformations correspond to rotation of the polarization basis by a prescribed angle which is a function of (1) the coordinate transformation matrix that relates the two coordinate frames and (2) the direction of propagation. Although methods for determining the polarization rotation angle have been presented previously in the literature, they can only be applied in special cases. Here we solve the problem in the general case using methods based on spherical trigonometry and vector algebra, respectively. In order to apply these techniques, the elements of the coordinate transformation matrix must be known. Since conventional methods for determining these elements requireinformation which may be difficult to obtain in practice, we present an alternative method which requires only a pair of directions that have been expressed in terms of both coordinate frames.