When Karen Dulong began planning her wedding last winter, she intended to say “I do” on March 8. She wanted to honor International Women’s Day and the sixth anniversary of when she told her partner that she really liked him.

So she called the City Hall in Copenhagen, where she and her partner live, as soon as registration opened to reserve a slot. Immediately, she was disappointed.

“When I called, it was already booked,” said Ms. Dulong, 28, who owns a gallery. “How could it be booked already?”

Ms. Dulong is hardly the only bride in Denmark to find City Hall overwhelmed. In recent years, a surging number of foreign couples have flocked to Denmark, in part because it requires fewer documents and has a more streamlined process than many other countries.

“There’s so many people from other countries coming to Denmark to get married — it’s really crazy,” said Cecilie Julbo, a Danish wedding planner, who said some of her local clients could not find a good time slot in Copenhagen.

The competition has grown so intense that Danish authorities have struggled to accommodate everyone who wants a civil wedding, prompting Copenhagen to announce in June that it would start reserving slots for locals.

That came after officials uncovered an embarrassing error. Since 2018, Copenhagen had inadvertently charged almost 15,000 couples, many of them foreign, about $3.6 million in illegal fees for their weddings.

Most of them were charged for City Hall weddings that were held outside of regular hours, through a service that the city had introduced to meet demand. But Danish law stipulates that everyone, including foreigners, must be allowed to marry at City Hall for free, Niels Peder Ravn, a City Council member, wrote in an email.

Copenhagen eliminated the fees. This month, the city budgeted money for refunds. It also added funds to increase the number of civil weddings from 8,000 to 10,000 next year.

But the mistake highlighted the strain that foreign weddings have put on the city and on residents who want a City Hall wedding.

“I can see, if you’re Danish, how it would be really frustrating,” said Leanne Hindle, the director of Marry Abroad Simply, which facilitates weddings in Denmark and elsewhere. “You pay your taxes and you live there, and you just can’t get married.”

Some officials and wedding planners want to restore those charges to help accommodate the demand.

“It adds great value to the city that so many internationals are getting married here, and clearly, they don’t mind paying a small fee for it,” Louise Theilade Thomsen, a member of Copenhagen’s City Council, wrote in an email.

There have always been free wedding slots at the City Hall, but some Danes have had to jump through hoops to snag one.

Ms. Dulong, the gallery owner, ultimately found someone to conduct her civil marriage to her now husband, Tobias Rytter, on her ideal wedding date. But Ida Rud, a Danish journalist and radio host, struggled to find a workable option for her civil ceremony.

In spring of 2023, after she became pregnant, she looked for a summertime slot: “I thought it could be kind of spontaneous,” said Ms. Rud, 43, who was living in Copenhagen.

There were no Saturdays free at the City Hall until November, well past her due date. They could have paid for a private registrar to officiate at City Hall, but “we didn’t feel like we could afford it,” she wrote in a WhatsApp message.

They booked the first Saturday available and hoped for the best. But as that date approached, her father-in-law entered end-of-life care. They canceled the wedding date. He died about a week later.

“We just couldn’t find a date that worked for us,” said Ms. Rud, who eventually married in September 2024. “We had to really compromise.”

For many foreign couples, a Danish wedding is a compromise, too: They cannot easily marry anywhere else.

Some are gay couples whose governments do not allow same-sex weddings. Some are refugees who cannot safely travel home to gather the documents other countries require.

Katsiaryna Abramava, a Belarusian who lives in Poland, would have had to get documents from Belarus, where she feared being arrested because of her political beliefs. So she married in Copenhagen. “It was the best day of our lives,” she said.

The smoother process is what pushed Jamie Kilbane, 42, who is Irish and lives in Berlin, to plan his wedding in Denmark, which became the first country to recognize same-sex unions in 1989. He and his now husband, Uli Lützenkirchen, also had friends in Copenhagen, so “it was the perfect mix of romance and practicality,” he said.

They also felt an urgency as the American right questioned same-sex marriage and German conservatives removed Pride flags from the parliament building.

So Mr. Kilbane said he barely thought about the 2,455 kroner (about $385) they spent for a private registrar to officiate at City Hall in July, which the city will probably now refund.

It was worth it, Mr. Kilbane wrote in a WhatsApp message: “I would pay it again in a heartbeat.”