Amelia opens in Miami, Florida, 1937, as Amelia Earhart (Hilary Swank) is about to begin her attempt to be the first person (male or female) to circumnavigate the globe. She is posing for photos with her new Lockheed Elektra aircraft, and bids farewell to all.
The movie flashes back to young Amelia, watching an airplane fly over a prairie field in Kansas. She vows to do that someday.
Skip ahead to 1928, where Amelia meets George Putnam (Richard Gere), in NYC. George is a promoter, who publishes and is basically a PR master. Amelia meets with George to procure a sponsor, as she wants to be the first female to fly across the Atlantic. George tells her that several have died in the process, so for his sponsors to agree to this, she'd actually be a passenger in the back of the plane with both a pilot and navigator flying it. Reluctantly, she agrees, as this will garner great publicity and funds for her to continue her flying career. During the discussion, it is obvious that the two are attracted to each other.
The first attempt to fly the trip on the aircraft "Friendship", beginning in Boston, is aborted. Later, the next day, they try again, and begin the trans-Atlantic flight. Amelia is in the back, and at one point, nearly falls out of the airplane when the door opens. The team finally sees land, and they successfully land the plane. They aimed for a landing in Ireland, but as the locals explained when they got out of the plane, they actually landed in Wales.
Amelia begins an exhausting tour of lectures, promotional stops, and product endorsements. She writes a book about her feat, and grows closer to George, whom she affectionately calls "GP". On a book tour, she goes to GP one evening in his hotel room, in her fur coat, and asks him to dance. When she is in his suite, she removes her coat, and is wearing silk pajamas. They dance, and spend the night together. This is the beginning of their relationship.
Soon, Amelia meets Gene Vidal (Ewan McGregor), and they strike up a friendship. She tells him she sees herself as a "vagabond of the air".
The next scene is NYC, 1931, and Amelia explains to George that although she loves him, she's never seen herself as the marrying kind. He apparently keeps asking, and she writes him a letter, and reads it aloud to him. She tells him that she cannot expect him, or herself, to remain faithfully by some archaic set of rules. They both must be free to leave or do what they want. She also asks that if they aren't blissfully happy in a year, for him to let her go. He agrees, and she becomes Amelia Earhart Putnam in a small outdoor ceremony.
Enter Eleanor Smith, a young female pilot that will be a competitor to Amelia, and yet Amelia never feels threatened. She just wants to promote female aviators and gives Eleanor advice: Never let anyone stand in your way. Soon, there is to be a big Air Derby for female aviators, and both women are entered, among others. As the event is about to begin, GP manipulates Eleanor into dropping out, so that female aviation can be advanced with the publicity of Amelia winning. Eleanor rebuts that Amelia told her not to let anyone stand in her way, and that he is doing that. He agrees, and yet gets her to drop out. At the end of the cross-country derby, Amelia comes in third. At the press conference, she announces that she and 98 other female pilots have started a group to promote and help female pilots, called "the 99's".
Now Amelia wants to fly solo across the Atlantic. She flies through a bad storm of rain and lightening, and it looks doubtful of her success, but she finally sees land, and lands in a sheep pasture. She was navigating towards Paris, to land there as Charles Lindbergh had, but is told by the shepherd there that she landed in Ireland. Her flight took 14 hrs and 54 minutes.
The endorsement deals keep coming, and she endorses luggage, clothing, and appliances. She doesn't like doing it at all, and calls herself a white horse jumping through hoops. GP reminds her that the money she brings in keeps her flying, which is very costly. She knows this, and is resigned to the fact that she must keep doing it.
Now, she has her hopes on a bigger, much more dangerous flight: to circumnavigate the globe. This is very dangerous and expensive. Nevertheless, she keeps this as a goal.
At a formal event, she is seated next the President Roosevelt's wife, and she is enamored with Amelia. She speaks of wanting to experience the thrill of flying herself, to which Amelia asks: "How do you feel about flying at night?" Amelia, GP, the First Lady and a handful of others bring some champagne and take flight over Washington DC. Amelia lets the First Lady take control of the plane, and they all have a wonderful experience.
Gene Vidal comes back, and asks Amelia, with all her good press and celebrity, to be his advisor in launching his Shuttle, flights from city to city, across the country. This is the first commercial airline effectively connecting the country by plane, around 1934. During this time, they begin an affair. She helps him care for his son, and they grow close.
Later on, GP find a love letter that Amelia had written to Gene. He reads it aloud to her on the phone, while she is away, and then hangs up on her. It becomes clear to Amelia that she is breaking his heart, and she is deeply saddened by this. She tells Gene that she is quitting as his advisor, that their affair is over, and that she is returning to GP.
George has been working to get funding for Amelia's flight, and has Purdue University ready to declare an Amelia Earhart School of Aeronautical Studies, and will provide $80,000, which is what she needs to buy the Lockheed Elektra, have it modified, and pay the expenses of the flight. Work begins, and she hires the best celestial navigator, Fred Noonan, to be the navigator for her flight and fly with her around the world.
Just before hey begin the flight, the press asks questions and takes photos, and then they taxi down the runway. The flight begins in Hawaii and will have the trickiest part at the beginning: trying to refuel at Howland Island, which is the only piece of land across the vast oceans. After that, it is much easier. Amelia is told that she isn't skilled enough to handle the risky mid-air refueling attempt, which is successful only about 20% of the time, with an experienced pilot. As they taxi, something is wrong with the plane, and Amelia aborts the take-off. The landing gear breaks off, sending the plane skidding on its belly down the runway. Sparks fly, and the engines begin to flame. Without Amelia's quick thinking and maneuvering safely down the runway and off onto some grass, they'd have been killed. They both are unharmed by the crash, but shaken up. The faulty landing gear has cost Amelia her dream flight...for now.
George gets funding and labor to repair the plane. By the time it is finished, it is later in the year, and Amelia realizes she must reverse the route of her trip and end in Hawaii, due to monsoons and seasonal changes. June 1st they take off, and the movie is back to where it began.
As Amelia and Fred fly, scenic shots of the landscape are shown, and she makes stops in Pakistan, India and New Guinea. While in New Guinea, Amelia and Fred wait for the rain to end in an open-air bar. Fred is drinking, which is a source of concern. He makes inappropriate remarks to Amelia, and she leaves. She then has her last conversation with GP, via radio. They talk about meeting for the 4th of July, and George can't wait until she's home. Amelia asks, "Where's home?" and he replies, "Anywhere you are". As they say good-bye, Amelia says their trademark goodbye of " See you, my darling" and George replies with, "See you, my love". This is the last time they will speak to each other.
The next morning, Amelia is throwing extra luggage out of the plane to lighten their load, and Fred apologizes for his remarks the previous day. She says it is ok, and she and Fred begin this segment of the flight. The ground control reports to George via radio, that the headwinds were stronger than they anticipated, so the flight will use 9% more fuel than it was supposed to. George looks concerned.
At Howland Island, the US Coast Guard Cutter Itasca is ready to assist Amelia, and has their radio on and is transmitting messages, trying to locate her. Their direction finder was left on overnight, causing the battery to run dead, and now they don't have a functioning one to help them locate Amelia. Amelia keeps transmitting messages, but cannot hear their responses; it seems her receiver isn't working. Without confirmation from the Coast Guard, Amelia has no way of knowing how close she is to that small, 2 mile-long island. It is overcast, so Fred's visuals aren't helping either. The Coast Guard tries transmitting in Morse code, not knowing she doesn't have the equipment to pick it up. They then send up a big black puff of smoke from their smokestack, which should be visible for 20 miles around, but Amelia doesn't see it. Amelia keeps transmitting, and intermittently, the Coast Guard at Howland can hear her, but she isn't transmitting long enough for them to get a read on her location. On July 2, 1937, Amelia Earhart and Fred Noonan and the Elektra vanish, and no sign of the aircraft was ever found.