Abstract: Systems and methods for locally engaging tissue using suction. In at least one catheter device embodiment, the catheter device comprises an engagement catheter having a proximal end, a distal end, and a vacuum lumen therethrough operably coupling the proximal and distal ends; an elongated tube of a shape memory material having a plurality of elongated strips removed from a length of the elongated tube to form elongated shape memory tines at a distal end of the tube, wherein the shape memory tines flare outward away from a central axis to form a fluted distal end; and an elastomeric coating disposed over the elongated shape memory material tines to form a suction cup shape.