Over the last decade, some of that business has moved elsewhere as companies hunt for cheaper labor and lower production costs, leaving many skilled workers without jobs. Now, a new generation of homegrown luxury entrepreneurs is building businesses that take advantage of that craftsmanship.

In Hungary, the contemporary women’s wear brand Aeron was founded in 2012 by Eszter Aron, its head designer, and three friends, with Vivien Laszloffy joining the business as chief executive in 2015. The label’s philosophy, Ms. Laszloffy said, is to be a brand “that people will recognize and know is from Budapest, in the same way people look at Acne and know it’s from Sweden.”

“People say it is against the odds to build a brand from here, rather than move to Paris or Milan, but actually we see it as an advantage,” she said. “Everyone has a vision in their minds of what a French or Italian brand looks like. But no one can imagine a brand from Budapest yet. And so we can seize that space and make it our own.”

As a privately owned company, sales figures are not released. But the two women said sales doubled annually in each of the last three years, with the majority of growth coming from an unexpected region: Asia.