How do you deal with your child’s first real rejection?

It is a question that Priscilla Sands, head of the Marlborough School, an elite girls school in Los Angeles, addresses every year when students learn they didn’t make it into their top colleges. She knows they are disappointed and distraught. She also knows that what looks like a setback might not be.

“It’s an issue for parents. They need to understand the pain, but also not rob their child of an opportunity to use it as a growth experience,” says Dr. Sands, who didn’t attend her dream college, worked in a diner as a single mom to support her children, and didn’t get jobs she thought she deserved.

By the end of March, most high-school students will have heard from colleges whether or not they have been accepted. Competition to get into top schools has been getting stiffer nearly every year. Many colleges and universities, including Yale University, Brown University, Duke University and Cornell, reported record high early application numbers for the class of 2021, according to IvyWise, an educational consulting company. Most students have until May 1 to decide where to go.

Claudia Vulliamy, of London, had several rounds of interviews and an overnight stay at Oxford University, where she wanted to study classics.

While hopeful, she prepared herself for bad news, but was “quite disappointed” when the letter from Oxford arrived saying she didn’t make it. She texted her mother, Louisa Saunders. “I thought, ‘Be ready to be sympathetic and feel disappointed on her behalf,’ ” says Ms. Saunders.

When Ms. Saunders arrived home, she said Claudia was “relatively chipper.” She had taken the Oxford letter and cut out key phrases—“after careful consideration” … “sorry not to have better news” …. “not been possible to offer you a place” … “no longer under consideration”—and incorporated them into a painting. “I suppose when you are rejected by something, your first instinct is to slightly mock it,” says Claudia, who called the painting therapeutic. Her mother called it “brilliant.”

Claudia wasn’t going to show it to anyone else, but when her mother reacted so positively, she decided to share it with friends on Facebook. “Then I won’t have to make an awful announcement that I didn’t get into Oxford,” she explains. Friends, who likewise received rejection letters, were cheered, says Claudia, who will either go to Durham University in England or take an art foundation course for a year. Her mother tweeted it, saying: “Yesterday, my daughter learned that she hadn’t got into Oxford. By the time I got in from work, she’d made this from her rejection letter.” It was retweeted about 52,000 times.

Diane Barth, a clinical social work psychotherapist, reminds parents that helping their child manage this disappointment will help when they don’t get the job or promotion they wanted, or are jilted by a girlfriend or boyfriend. “There are a lot of disappointments in life and this is an important one to help kids learn that while painful, they aren’t the end of the world,” she says.

Anisha Shah, a 19-year-old freshman at Washington University, who attended the Marlborough school, discovered just that. She was crushed when she didn’t get into Yale, but remembers her parents’ comforting message, the most important being it wasn’t about her, or anything she did or didn’t do. It was more that Yale wasn’t the right place for her particular talents. Her dad likened her to a “trumpet player” and said Yale didn’t need a trumpet player in its freshmen class but that another school did and when she found that school, it would be the perfect fit. He had also suggested she make a private list of pros and cons after every college tour, something only she would see, allowing her to be perfectly honest with herself.

Marlborough’s Dr. Sands remembers when her son didn’t get into his top school. She told him that the school missed out on someone wonderful. “That’s not the worst thing for parents to say,” she says.

She says it is important for parents to acknowledge their child’s sadness, but not assume it. “Your child wants you to feel sad, but they want parents to be the adults,” she says. Also, parents need to be wary and not interpret the rejection as a criticism of their parenting skills.

Dr. Sands says not getting into the “best school” in terms of rankings can lead to choices and experiences that are rewarding in the long run, something she herself discovered. After high school, she says she “sort of bounced around and didn’t know what I wanted to do.” She took continuing education classes at a junior college. When her then-husband, who was in the military, was stationed in Panama, she left school, went with him and started a dinner theater, which didn’t require a college education.

Later, when he was out of the military, she wanted to attend Brown University and study theater arts. Instead she went to, and graduated from, the University of Rhode Island because her husband taught there and tuition was free.

She waitressed, wrote for a local newspaper and taught theater to support her children after getting a divorce. Dr. Sands ended up moving to North Carolina, where she directed plays, and ended up teaching drama at a private girls’ school in Pennsylvania, where her mother was headmistress. She eventually realized she wanted to become a school administrator and run her own schools and obtained her doctorate in educational leadership from the University of Pennsylvania.

“I talk with parents and the girls about how my life took all sorts of twists and turns, how I was disappointed and didn’t go to the college I wanted or get the job I wanted,” she says. Each disappointment, she tells them, put her on a new path forward.