this is an old classic movie Portrait of Jenny..

A fantasy. Joseph Cotten meets Jenny who is a young girl, then in subsequent meetings she ages at each meeting. Then she's a young lady. He finds out that she died years before in a tidal wave on an island called Land's end. I'm sure in an earlier scene she tells Jos. Cotten she's leaving for Maine for the summer. Later he finds out the day she died in a tidal wave, and wants to save her from her death. When he leaves he tells someone he's going to an island off Cape Cod. The Cape is in Massachusetts not Maine.