The food served is substantial and decadent; several visitors mentioned poached lobster as a favorite.

Strawberries, the traditional snack of Wimbledon, are also offered, but not merely those sold to other fans on the grounds. Royal box guests enjoy an especially exquisite variety, called a Driscoll Jubilee, which is treasured for its firmness and sweetness and reserved for their consumption.

The group adjourns to the court 10 minutes before the first match begins and stays there throughout the day. Afternoon tea is served from 3:45 p.m. to 5:15 p.m. For those wanting further nibbles, a small leather-bound bucket of candies is discreetly passed through the box during play. If it becomes chilly, as it often does, blankets arrive.

Guests are assigned woven-wicker seats in the box, each with their name, a commemorative program and a small gift. This year, the gift was a green leather zippered bag embossed with the Wimbledon logo and the words “Royal Box 2017.” Guests also receive sterling silver lapel pins and a commemorative photograph of match action from that day’s play with the box visible in the background, paired with a seating chart.

More than the amenities, what guests treasure most is the company. Ken Solomon, the chairman and chief executive of Tennis Channel, called it “a cross section of the most interesting people who are in the U.K. at that moment.”

Solomon said he could only compare the camaraderie of the shared experience at Wimbledon to what he has felt as a guest of the American president.

“When you meet someone at the White House, it doesn’t matter who they are — you know they are having one of the greatest days of their life as well,” Solomon said. “No matter who you are, how important, you can’t buy your way into that space, and there’s only a handful of people who are there, and it’s very special. You’re going to remember it the rest of your life, and you know they are, too.”