Utilizing the so-called vector phase of polarized light, both focal-plane coronagraphs (e.g. the Vector Vortex Coronagraph) and pupil-plane coronagraphs (e.g. the vector Apodizing Phase Plate) are powerful components for high-contrast imaging. These coronagraphs can be built and optimized with polarization techniques and liquid crystal technology, that enable patterning at the micron level and furnish broad-band performance. The contrast between the residual starlight and the (polarized) reflected light off exoplanets can be further bridged by incorporating sensitive, dual-beam imaging polarimetry. As vector-phase coronagraphs use polarizers to enhance their performance, we introduce optimally integrated solutions that combine advanced coronagraphy and polarimetry. For both the VVC and the vAPP we present polarization beam-splitting concepts, with polarization analyzers either behind or in front of the coronagraphic optics. We discuss design solutions for the implementation of polarization optics, and set the stage for a trade-off between the improvement of coronagraphic and polarimetric performance and the ensuing degradation on the high-contrast imaging performance due to wavefront errors.