Catheters and methods are provided for performing medical procedures, such as tissue ablation, adjacent the ostia of anatomical vessels, such as pulmonary veins. The catheter comprises an elongated flexible integrated catheter body having proximal and distal shaft portions and at least one operative element carried by the distal shaft portion. The distal shaft portion has a proximal section configured to be internally actuated (e.g., using a steering mechanism or pre-shaping the proximal section) to form a simple curve with an apex that can be inserted into the vessel ostium, an intermediate section pre-shaped to form a curve that bends opposite the simple curve, and a distal section configured to be placed into a non-radial relationship (tangential or oblique) with the vessel ostium when the apex of the simple curve is inserted into the vessel ostium. By this arrangement, the operative element is configured to be placed firmly in contact with tissue at a predefined radial location relative to the vessel ostium when the apex of the simple curve is inserted into the vessel ostium.