The Röntgens’ homestead, called Campanula, is a 10-minute walk downhill from the train station. Originally built by a farmer in 1904, the rustic dwelling housed pigs on the lower level, which opened to his 40-square-meter patch of sun-dappled grassland. The house overlooks the stunning expanse of the Lauterbrunnen Valley, which may have inspired Tolkien’s fictional elven realm of Rivendell.

Mr. Röntgen’s German-born maternal grandmother bought Campanula as a vacation property from its second owner, the Swiss artist Anna Spühler, in 1924. Mr. Röntgen fondly recalls regular boyhood visits, when the home featured a big ceramic stove in the living room. He befriended local children, took ski lessons and spent hours at the municipal pool.

In April 2016, six months after relocating to Wengen, the Röntgens began an extensive renovation. The couple hired the same local architect they once used for kitchen remodeling and moved to a rental apartment in a chalet on Wengen’s main street for seven months. They were particularly keen to remove an interior wall that blocked the Jungfrau, which they could see only from the porch. They decided to raise the heights of their ceilings on two floors, vault the ceiling on the third and replace the outside balcony. Their open-plan living space design included a galley kitchen from the Dutch Mandemakers Group. They also mapped out four bedrooms, three and a half bathrooms, a laundry and a vestibule.

At the time, the cost estimate was $700,000, which included a number of helicopter deliveries. Wood ceiling beams were too long to fit around the curve of the mountain railway tunnel. Helicopters also hauled away debris, which was too unwieldy to take to the rail station in an electric cart. Because local laws prevented tampering with the exterior footprint, the Röntgens kept the lower terrace level entrance separate with no internal connecting staircase. As a guest bedroom with its own bathroom, it would be reached from the descending staircase in the porch.