"The pilot, Tammy Jo, was amazing!" Amanda Bourman, a passenger on Southwest flight 1380 posted on social media.
Shults "came back to speak to each of us personally," wrote Diane McBride Self on Facebook. "This is a true American hero. A huge thank you for her knowledge, guidance, and bravery."
A friend in contact with Shults since Tuesday's incident told ABC News that "she is doing fine." Shults was said to be undergoing routine tests conducted after flight mishaps to ensure that pilots did not have any drugs or alcohol in their systems.
While a lot of attention has been focused on the flight skills she and her co-pilot exhibited in safely landing the plane, Shults is said to be more concerned about the passengers on her flight.
The friend said Shults's thoughts are with Jennifer Riordan and her family. Riordan was the sole person killed in Tuesday's incident, dying from injuries suffered after the Boeing 737's engine came apart.
Shults is not only an experienced pilot with Southwest Airlines, but she was also among the Navy's first female fighter pilots.
"She was commissioned in the Navy on June 21, 1985, and completed flight training in Pensacola," said Lt. Christina Sears, a Navy spokesperson.
"She served at the Tactical Electronic Warfare Squadron (VAQ-34) in Point Mugu, Calif. as an instructor pilot flying the EA-6B Prowler and F/A-18 Hornet," Sears said.
"We can confirm that Lieutenant Commander Shults was among the first cohort of women pilots to transition to tactical aircraft," Sears said.
The New Mexico native remained on active duty with the Navy until 1993 when she transitioned to the Naval Reserve and retired in 2001 with the rank of Lt. Commander.
Shults was trained as a Navy fighter pilot at a time when female pilots were not allowed to fly with combat units.
After graduating from flight school in 1989, Shults served with Tactical Electronic Warfare Squadron 34 (VAQ-34) from 1989 until she left active duty in 1993.
But like the other first female Navy pilots trained to fly on the F/A-18 Hornet, Shults was assigned to fly the fighter aircraft in an electronic warfare training squadron instead of flying with units assigned to aircraft carriers like their male counterparts.
In March 1993, she was among the VAQ-34 squadron pilots interviewed by the Navy's All Hands magazine.
“In AOCS [Aviation Officer Candidate School], if you’re a woman [or different in any way], you’re a high-profile; you’re under more scrutiny,” Shults was quoted in the article.
“It would be nice if they would take away the ceilings [women] have over our heads,” Shults said.
“In VAQ-34, gender doesn’t matter there’s no advantage or disadvantage,” she said. “Which proves my point - if there’s a good mix of gender, it ceases to be an issue.”
Shortly after that article was published, Defense Secretary Les Aspin lifted the restrictions on female pilots flying combat missions. But by then Shults had already left the active duty Navy.
Shults also spoke about the difficulties she and other female Navy aviators faced in the 1998 book "Call Sign Revlon: The Life and Death of Navy Fighter Pilot Kara Hultgreen" written by Sally Spears, Hultgreen's mother.
A friend of Shults's, Hultgreen was the first female Navy pilot certified for combat duty. She was killed in October 1994 crash while attempting a landing on the aircraft carrier USS Abraham Lincoln.
In the book, Shults noted that Navy commanders tried not to show female pilots special treatment, but their actions sometimes had the opposite effect on male pilots.
"Like they would have the women in for coffee and cookies with the captain," said Shults. "It made us feel like idiots. I mean, nobody has coffee and cookies with the captain."