I haven't seen this for ages, so I might be offbase. Here's what came immediately to mind:
A Separate Peace (1972) From IMDb: Gene (Parker Stevenson in his film debut) and Finny (John Heyl in his only film appearance) are two boys who are best friends living in 1943, at the height of World War II. The idea that the boys most likely will be drafted when they turn 18 is surrounding them, and they are practically forced to live their lives to the fullest. The two boys attend the Devon School, which prepares them for military life that they might be subjected to. The film begins with a narration by an older Gene, traveling back to Devon some years later. The thing he wishes most to see is the tree that had a great effect on the boys' lives.
This is just a guess because of the tree and the vow.