Described, in certain respects, are unique methods and systems for treating fistulae and other passageways and openings in the body. In some embodiments, treatment will be performed on fistulae that include a passage extending through a subcutaneous wall or wall-like structure. Illustratively, such a passage can extend through a subcutaneous tissue wall that includes, at a minimum, portions of an intestinal wall, and in this regard, such a wall can have a first side that is provided by the luminal side of the intestines and a second subcutaneous side that is provided, for example, by the abluminal side of the intestines and/or by other subcutaneous tissues adhered to this abluminal side. Some inventive products and methods involve sealing off the passage from both sides of the wall, for example, where a sealing element is placed on each side of the wall over an opening to the passage.