Serendipity (2001)

Sara (Kate Beckinsale) and Jonathon (John Cusack) meet in New York City during the Christmas season and both want to buy the same pair of gloves. Jonathon gallantly allows Sara to buy them and she takes him out for ice cream in thanks. They spend the evening together ice skating and talking and have such a connection that Jonathon pleads with Sara to at least exchange names and numbers so they can keep in touch. Sara relents but the paper with her name is blowqn out of her hand, and she, superstitious by nature, decides it was a sign they were moving too fast. Instead she has Jonathon write his name and number on a five dollar bill and uses it to buy gum. She promises to write her own name and number in the book "Love in the time of Cholera" and sell it to a used bookstore. When they find these items again, they will know they are meant to meet up.
A year later, Jonathon is getting married to another girl, Hallie, and Sara is engaged to a musician, but neither has forgotten the other and with the encouragement of their friends, and their weddings looming as deadlines, they end up in New York searching for each other once more, hoping for a sign that they are really meant to be.