A catheter for mapping and/or ablating continuous linear or circumferential lesions at the intersection of a generally flat structure, such as the left atrium, and the ostium of generally cavernous regions of the heart, including pulmonary vein and the pulmonary venous antrum, comprises a catheter body with an intermediate section that is connected to a tip assembly by a highly flexible section. The intermediate section has at its distal end a preformed section, e.g., a curve, the intermediate section being deflectable in a direction opposite to the curve. The highly flexible section presets the tip assembly at an off-axis and/or off-plane angles from the preformed section. Accordingly, the preformed section is adapted to sit in the region and the preset angles of the ablation assembly enable contact with surrounding tissue. A high bending modulus enables the flexible section absorb displacement force applied to the ablation assembly, such as when the tip assembly encounters uneven tissue surface, without displacing the curve from the region. The tip assembly can be irrigated as enabled by a plurality of irrigation ports, a coil electrode, and a porous covering to disperse fluid over the outer surface of the tip assembly.