No one likes to be stuck in a long, slow-moving security line at the airport. Unless you meet the person you’re going to marry.

That’s what happened to Josh Mankiewicz and Anh Tu Dang in 2009 at the Los Angeles International Airport, thanks to Transportation Security Administration procedures.

“Standing ahead of me was this stunning woman,” Mr. Mankiewicz said. “I was staring at her. She didn’t notice. Finally we started talking. Actually, I started talking and she responded.”

Ms. Dang figured there was nothing else to do. She recalled thinking: “He seemed kind of nice. I may as well talk to him.”

Their conversation was brief and friendly. Luckily, Mr. Mankiewicz, a correspondent since 1995 for the NBC News magazine program “Dateline,” could read the upside-down tag hanging from Ms. Dang’s bag.

Unluckily, when he returned to Los Angeles from his business trip and searched for her name on Google, he found several Anh Tu Dang’s, just not the one who had caught his attention.

But Mr. Mankiewicz, who had never married, had impulsively given his business card to Ms. Dang, who was divorced and the owner and chief executive of the home health care business CareWorks Health Service in Laguna Hills, Calif. “I was 100 percent sure I would never hear from her and that what I had done was something silly and overconfident,” he said.

Once Ms. Dang returned to Los Angeles from her trip and looked up Mr. Mankiewicz, she was worried that he may have a big head and big ego. “He might have girlfriends in Chicago and New York, and I didn’t want to be another person on that list of women,” she said.

After about four weeks, she decided to call. “He was handsome and apparently smart,” she said. “I thought, let me give it a shot and see what happens.”

When Ms. Dang, 42, identified herself as the woman from the airport, Mr. Mankiewicz, 60, didn’t immediately recognize who was calling. “I wondered if maybe I’d lost something,” he said. But when he realized it was Ms. Dang, whose nickname is Tee, he quickly invited her to dinner.

“I remember walking into the restaurant and being struck by how beautiful she was,” Mr. Mankiewicz said.

The couple dated for over a month, but not exclusively, and then Mr. Mankiewicz decided to pursue another relationship. “I wasn’t the right fit for him,” Ms. Dang said. “You know how you can tell when a guy’s heart isn’t into it.”

“She let me off the hook pretty easily,” he said.

Then one day, four years later, in summer 2013, Mr. Mankiewicz, who had months before broken off his previous relationship, found himself on the street where Ms. Dang lived. He called her and they met for lunch.

“Not to say we were boyfriend and girlfriend from that day forward, but I was definitely smitten,” he said. “I always wanted someone who could stand up on her own and stand up to me, someone who didn’t need me but wanted to be with me, and that was Tee.”

Mark Thompson, a Los Angeles newscaster who has known Mr. Mankiewicz since childhood, said his friend has been with some women in the past who were “into drama.” “She is the opposite,” Mr. Thompson said. “She is not looking to litigate every cup of espresso.”

Despite their age difference (“She’ll say, ‘I remember when this song came out, I was in the seventh grade,’” he said. “And I’ll say, ‘I was covering the Mondale campaign.’”), they found compatibility in their professions.

On “Dateline,” Mr. Mankiewicz speaks to people whose family members have been murdered. In her home health care business, Ms. Dang speaks to people who have often undergone devastating physical or mental losses.

“We’re both in roles where we are talking to people who are dealing with sadness and trauma, and they need compassion and understanding,” she said. “Reaching people at an emotionally fragile time gives us something in common and helps us be sensitive to one another.”

Five weeks after they had begun dating again, real drama emerged in their relationship. Ms. Dang received a diagnosis of breast cancer and she subsequently had a double mastectomy.

Mr. Mankiewicz insisted she recuperate in his two-bedroom Beverly Hills condominium (ultimately she would have eight operations) in spite of her protestations that she could stay at her own place and simply lie on her couch, have the pharmacy deliver medicine and order takeout food.

“She comes off as 10 feet tall and bulletproof,” Mr. Mankiewicz said. “But she needed my help, and I wanted to help her. This told me things about myself and my relationship to her, namely that I was in love with her in a way I hadn’t realized.”

The operations forced Ms. Dang to acknowledge her vulnerabilities. “I was crying — this is hard,” she said. “I wasn’t expecting this to happen to me at 39.”

And the recovery experience left her exposed to Mr. Mankiewicz in a way she hadn’t planned. “I couldn’t be Superwoman-hear-me-roar,” she said. “I hadn’t showered in days. My hair was a mess and I had tubes coming out of my body.”

After she recovered, she moved back to her Santa Monica apartment, but this time he was not letting go, and she felt safe. “I could tell him anything, and he wouldn’t judge me,” she said. “He can see through me like a pane of glass and read me better than anybody else.”

The couple could hardly have come from more different backgrounds. Mr. Mankiewicz’s grandfather, the screenwriter Herman J. Mankiewicz, shared an Academy Award for writing “Citizen Kane.” His father, Frank Mankiewicz, was press secretary for Senator Robert F. Kennedy, presidential campaign manager for George McGovern and president of National Public Radio.

“I grew up with this front-row seat to national politics,” Mr. Mankiewicz said. “Every conversation with my dad was like opening a history book. I met Robert Kennedy a few times. George Cukor sat at our dinner table. I watched a lot of TV news, and Vietnam played out in my living room. I was interested in being a news reporter since I was 10 years old.”

By contrast, when bombs were falling on Saigon in 1975 and Ms. Dang was 1½ years old, her mother, then eight months pregnant with Ms. Dang’s brother, escaped to Guam by boat. The family, later joined by Ms. Dang’s father, Khoi Van Dang, who was disabled when Ms. Dang was 13, settled in Orange County, Calif., where they became naturalized citizens.

“My family did not allow me to watch TV during the week unless it was something on PBS and probably about an elephant,” Ms. Dang said. She was a shy, motivated student. By sixth grade she was reading at a 12th-grade level. “It was easy for me to go into my room, spend the day there reading and come out at 6 at night,” she said.

Mr. Mankiewicz takes their cultural differences in stride. “My dad is from a successful Jewish family, and my mom, who had been raised a Mormon, was the first member of her family to attend college,” he said. “The lesson my parents gave me was: You don’t have to have a lot in common with someone to love them.”

From her perspective, Ms. Dang believes the Vietnamese culture can be tough on daughters. “Subconsciously it is ingrained that you need to take care of your guy,” she said. “Josh likes it that, for lack of a better word, I am not subservient.”

Joey Dang, Ms. Dang’s brother, saw another, possibly more lighthearted connection: They both love clothes and fashion. “Tee used to take pictures of her shoes and put them on the outside of the boxes,” Mr. Dang said. “As soon as I saw his closet, I thought, This is a man who gets my sister.” (Mr. Mankiewicz’s closet is color coordinated, with his jackets evenly spaced.)

After one year of steady dating, Mr. Mankiewicz was not making a move toward the altar. His father, who met Ms. Dang on his 90th birthday in 2014, told his son he should marry her. But his son balked: He wasn’t interested in having children. He was afraid if he was a part of someone else, he wouldn’t be himself anymore. And, he joked, “Dateline” was not the biggest commercial for matrimony.

The following year, Mr. Mankiewicz changed his mind about staying single, perhaps, as his brother Ben Mankiewicz, a host of Turner Classic Movies, suggested, because four events converged: Ben had a child; their father died; their aging mother had moved to Los Angeles; and his big brother had met the right woman. “It’s a testament to his emotional maturity that it was O.K. to change his life at 60,” Ben Mankiewicz said. “It took courage. It’s hokey to say, but I’m proud of him.”

Their mother, Holly Howell, said: “All I could say to myself was, it’s about time. He was seeing her a lot and I thought, if he doesn’t hurry up, she’d say to hell with it.”

In November 2015, at the restaurant where they’d had their first date, Mr. Mankiewicz proposed to Ms. Dang. “She gasped like someone in the movies I grew up watching,” he said. “We made a champagne toast and took a picture and then we sat there silently texting.”

The wedding was set for what would have been the 92nd birthday of Mr. Mankiewicz’s father. Eight weeks before, after the last of her operations, Ms. Dang moved in to Mr. Mankiewicz’s condominium. He lamented having to give away 220 of his shirts to make room for her clothes in his closet.

On May 16, they were married before a small gathering of family and friends on the deck of the home of Mr. Thompson, the retired newscaster, who became a Universal Life minister to officiate.

“Sometimes the path to love is slow, sometimes — courtesy of T.S.A. — it is excruciatingly slow,” Mr. Mankiewicz said. “But I suppose we should thank them. It gave us time to have that first talk.”

His mother delighted in the two families’ newfound connection.

“He finally came to his senses,” Ms. Howell said. “I mean it. You have to work really hard not to like her. There’s not an ounce of snobbishness in her. She doesn’t think she’s a big shot. She has views of her own.”

Ms. Dang’s mother, Ahn Thi Le, was sold on her new son-in-law at hello. “I’m a Buddhist. My house is a Buddhist temple,” she said. “The first time he came to visit me, he said, ‘Thank you for creating your daughter.’ He touched my heart right away. For her, I thought, you don’t have to find another person. You found him. Eureka!”