An apparatus for mapping and/or ablating tissue includes a braided conductive member that may be inverted to provide a ring-shaped surface. When a distal tip of the braided conductive member is retracted within the braided conductive member, the lack of a protrusion allows the ring-shaped surface to contact a tissue wall such as a cardiac wall. In an alternative configuration, the braided conductive member may be configured with the distal portion forming a proboscis that can be used to stably position the braided conductive member relative to a blood vessel, such as a ventricular outflow tract. The braided conductive member has a plurality of electronically active sites that may be accessed individually for stable mapping over a broad area for stable mapping or ablation to form broad and deep lesions.