The electromagnetic field within an aperture in the wall of a blackbody cavity is a known example of a Lambertian source producing a far field which is unpolarized in all directions. In this work we show that in the electromagnetic context other Lambertian sources exist whose far fields, while obeying the cosine law for the radiant intensity, differ by their polarization states and degrees. For example, the far field may be azimuthally, radially, or circularly polarized, or the polarization state may vary depending on the direction. For specific Lambertian fields generated by quasihomogeneous sources it is possible to calculate explicitly the 3×3 electric cross-spectral density matrix of the nonevanescent part of the source. This enables one to assess the source's spatial coherence and partial polarization properties. In all cases, the coherence length turns out to be roughly half a wavelength, whereas the polarization characteristics of the sources may differ significantly. Our results could find uses, for instance, in radiometry and photometry, lighting applications, and remote sensing.