The development of improved ductile damage models for plastically anisotropic materials has received limited attention in the literature. We derive a new yield criterion for materials containing spheroidal voids embedded in a Hilltype orthotropic matrix. The coupling of void shape evolution with the plastic anisotropy of the matrix leads to improved predictions for the yield surface as well as the evolution of microstructural variables. An alternative numerical approach is also developed to derive rigorous upper-bounds to the yield loci for anisotropic porous materials of a given microstructure. Under conditions of transverse isotropy, i.e. spheroidal voids in a transversely isotropic matrix, and axisymmetric loading, the numerical approach delivers quasi-exact results. Comparison of the analytical and numerical yield loci for selected material properties indicates significant improvements with respect to previous models from the literature.