The invention modifies the pericardium to treat patients suffering from or at risk of heart failure of the type wherein constraining forces of the pericardium around the heart are inadequate to prevent remodeling of the heart. The pericardium is enhanced by restoring, increasing, or improving its ability to restrain the heart and prevent dilation of the chambers of the heart. Methods and apparatus are provided for stiffening, strengthening, tightening, reshaping, and/or shrinking the pericardium to enhance the restraining and supporting capability of the pericardium around the heart. Specific embodiments enhance the pericardium by heating the pericardial tissue using radiofrequency energy and the like, treating the pericardium with a chemical such as glutaraldehyde, plicating the pericardium, or some combination of the above.