Apparatus and methods for an endovascular catheter that can be inserted within tortuous body anatomies and then selectively stiffened and fixed in place. In a particular embodiment, this stiffness is reversible. The stiffness or a comparable mechanical characteristic of the catheter assembly may be adjusted to a relatively low value during insertion (so that it easily navigates a guide wire or the like), and then subsequently adjusted to a relatively high value in situ to keep the catheter assembly substantially fixed in place (i.e., during delivery of an interventional device).