Flight 1380 was headed from NY to Dallas last month when an engine on the Boeing 737 exploded at 30,000 feet. She died later from her injuries.
After the window was shattered, the cabin was depressurized for 20 minutes as wind and debris swirled around passengers.
However, the pilot, Tammie Jo Schults, successfully landed the plane without further loss of life.
Trump hailed the pilot for doing an "incredible job" landing the aircraft.
One of the first women to fly fighter jets for the U.S. Navy, some close to Shults have called her the best pilot they've ever known.
On the chaotic flight, several passengers rushed to aid Riordan, a mother of two, who was partly sucked out of a window near the failed engine. Southwest sent each passenger a $5,000 check and $1,000 flight voucher.
"I'm trained for emergency situations and that's just exactly what it was, and I felt moved to act as well as other people on that plane", Needum said at a news conference last month.
National Transportation Safety Board (NTSB) chairman Robert Sumwalt said it was the first passenger fatality in a USA airline accident since 2009. They are also reviewing data from the airplane's cockpit voice recorder and flight data recorder, according to The New York Times.
National Transportation Safety Board investigators examine damage to the engine of the Southwest Airlines plane that made an emergency landing at Philadelphia International Airport in Philadelphia on Tuesday.