Methods and systems for securing tissues, e.g., cardiovascular tissues, are disclosed. A method in accordance with one embodiment of the invention includes inserting a portion of a catheter into an opening between a first portion of cardiovascular tissue and a second portion of cardiovascular tissue. The method can further include drawing the first and second portions of the cardiovascular tissue into contact with each other by drawing a vacuum in a region adjacent to the first and second portions of cardiovascular tissue via the catheter while the catheter is positioned between the first and second portions. The tissue portions can be fused by heating the tissue from within the opening, e.g., via radio frequency energy. This technique, and associated catheter system, can be used to close a patent foramen ovale or other openings in cardiovascular tissue.