An open weave fixation device is secured to a distal end region of a catheter or other diagnostic or treatment device, for either temporarily or permanently fixing the device within a body cavity. In one approach, the fixation element is constructed of braided, helically wound filaments of resilient stainless steel. A sheath surrounds the catheter and fixation element to elastically deform the element into a reduced radius configuration to facilitate insertion and deployment. With the fixation element positioned as desired, the sheath is withdrawn to permit the fixation element to self-expand against body tissue, thus to secure the fixation element and catheter. In an alternative arrangement, a dilatation balloon surrounds a catheter near its distal end, and in turn is surrounded by a plastically deformable fixation element. Following desired positioning, the balloon is dilated to permanently deform the fixation element into contact with body tissue. In either case, the fixation element can be mounted at its distal end, its proximal end or medially, depending upon the particular treatment and the expected duration of fixation. Another approach employs a recovery metal in the fixation element.