There are both woody perennials and herbacious perennials but I asume you mean herbaceous. I have never seen a herbaceous list of perennials resistant to verticillium wilt. Some perenials that I grow and do not get this disease (they get other diseases) are cone flowers, black-eyed Susans, yarrow, daylilies, mums, shasta daisies, phlox, astilbe, coreopsis and columbine.
