Message in a Bottle (1999)

During her morning jog on the beach, journalist Theresa Osborne (Robin Wright Penn) discovers a bottle protruding from the sand. Inside it, she finds a heartbreaking, anonymous love letter. After her paper publishes the letter, Osborne tracks down the letter's reclusive author, world-weary widower Garret Blake (Kevin Costner), in the Carolinas. But, as Osborne finds herself falling hopelessly in love with Blake, she becomes wracked with guilt over the real impetus for her visit.