Tissue eversion apparatuses and methods suitable for use, as examples, with vascular closure devices. The tissue eversion apparatuses comprise a tissue engaging element, disposed within a delivery sheath. The delivery sheath protects the tissue engaging element and the surrounding tissue during use. The tissue engaging element can extend from the sheath and engage the tissue near an aperture in a tissue wall. Motion of the tissue engaging element away from the tissue can urge the tissue wall near the aperture to evert from the tissue wall, allowing, as examples, aperture closure apparatuses and methods to be conveniently employed.