On July 2, 1937, Amelia Earhart (Swank) and her navigator, Fred Noonan (Eccleston), are on the last leg of an around-the-world flight. Moving in vignettes from her early years when Earhart was captivated by the sight of an aircraft flying overhead on the Kansas prairie where she grew up, her life over the preceding decade gradually unfolds. As a young woman, she is recruited by publishing tycoon and eventual husband George Putnam (Gere) to become the first woman to cross the Atlantic Ocean, albeit as a passenger. Taking command of the flight results in a success and she is thrust into the limelight as the most famous woman pilot of her time. Putnam helps Earhart write a book chronicling the flight, much like his earlier triumph with Charles Lindbergh's We, gradually falling in love with his charge, and they eventually marry, although she enacts a "cruel" pledge as her wedding contract.
Embarrassed that her fame was not earned, Earhart commences to set myriad aviation records, and in 1932, recreates her earlier transatlantic flight, becoming the first female pilot to fly solo across the Atlantic. Throughout a decade of notoriety, Earhart falls into an awkward love affair with pilot and future Federal Aviation administrator Gene Vidal (McGregor). In a display of romantic jealousy, Putnam quietly tells Amelia that he does not want Vidal in his house. Earhart is annoyed by the seemingly endless agenda of celebrity appearances and endorsements but Putnam reminds his wife that it funds her flying. They each acquiesce to the other's wishes and Earhart is drawn back to her husband on the eve of her last momentous flight, a round the world flight fraught with perils. Earhart's first attempt ends in a runway crash in Hawaii, due to collapsed landing gear. Earhart shuts off the fuel supply but her aircraft requires repairs before the flight can be attempted again. Eventually, she takes the repaired Lockheed Model 10 Electra "Flying Laboratory" in a reverse direction, leaving the lengthy transpacific crossing at the end of her flight.
Setting out to refuel at tiny Howland Island, radio transmissions between USCGC Itasca, a Coast Guard picket ship, and Earhart's aircraft reveal a rising crisis. Earhart radios to Itasca that the sky has become cloudy and overcast. When Itasca attempts to radio her back, however, all Earhart gets is static. For the rest of the approach, Earhart cannot hear Itasca's transmissions, although they can hear hers. The Coast Guard radio operators realize that they do not have sufficient length to provide a "fix". Itasca has a directional finder with a dead battery, and weak radio communications prevent Earhart and USCG Itasca from making contact. Running low on fuel, Earhart and Noonan continue to fly on over empty ocean, as Earhart informs the Itasca that she is on position line 157-337, running north and south. She is not heard from again. A massive search effort is unsuccessful, but solidifies Earhart as an aviation icon.