A “secret” celebrity wedding: In the age of social media, it seems like a Hollywood oxymoron on the order of “late-career comeback” and “no-fault divorce.”

Even so, to judge by the number of celebrities trying off-the-grid nuptials, far from the prying lenses of the paparazzi (Jennifer Aniston and Justin Theroux, married Aug. 5 in a quiet ceremony at their home in the Bel-Air section of Los Angeles, are but the latest), the underground wedding has become one of Hollywood’s biggest status symbols.

Cameron Diaz and Benji Madden, Johnny Depp and Amber Heard, and Zooey Deschanel and Jacob Pechenik are among the many couples to attract intense media speculation over their stealth unions, which generally managed to unfold in private without the tabloid scrum.

The famous friends who earn coveted invitations seem to acknowledge that, among the celebrity class, the No. 1 wedding gift on every registry these days is silence.

“I’m afraid to even talk about that wedding because everyone is on top-secret lockdown,” Howard Stern, a guest at the Aniston-Theroux ceremony, said on a recent SiriusXM broadcast. (“Howard Stern discretion,” of course, is another oxymoron; the Medusa-haired shock jock promptly let slip that Jimmy Kimmel had presided over the ceremony.)

No matter how much stars try to hide under the dome of silence, leaks are inevitable.

Ms. Aniston and her Ducati-loving husband, for instance, tried a major head-fake before their ceremony, reportedly hiding their party gear in a vacant house next door and telling guests they were being invited to Mr. Theroux’s 44th birthday party, not a wedding.

But within days, the tabloid-hungry public already knew about the guest list (which included Lisa Kudrow, Orlando Bloom and Lake Bell), Ms. Aniston’s dress (summery, boho-inspired) and their cake (Muppets-themed).

TMZ and People published numerous photos of the backyard setup, taken from high overhead, and grainy shots of a vendor carrying the cake. But no photos have emerged of the couple themselves, denying the gossip-hungry public even a mental image of the affair, the kind that can linger for years after, say, a royal wedding.

The truth is, the best efforts of the stars are not enough. Even the most discreet wedding is a team effort, so it comes down to the wedding planners, charged with overseeing the whole affair, to make sure that everyone, guests included, observes the lockdown.

“There’s no midpoint: It’s absolute secrecy, or it’s everywhere,” said Marcy Blum, the planner for several celebrity weddings, including LeBron James’s 2013 hyper-private event (the printed invitations did not even list a time or place). “Because of cellphones, TMZ doesn’t have to stake out a wedding for there to be a leak. Everyone’s an investigative reporter.”

Here are a few A-list planners discussing the new rules of the hush-hush celebrity wedding. (The following interviews have been edited and condensed).

In Weddings, Too, It’s Location, Location, Location: “The secret is, look for venues that are hard to get to. Anything with ocean access is easier to get to for the press. If secrecy is really a problem, do it inside a building. Then the chances of people seeing it are a lot less. Or you can use a tent. But sadly, there lies the problem. How do you make it beautiful and romantic without compromising the vision by having to cover it all up?” — JoAnn Gregoli, an owner of Elegant Occasions in New York.

Keep Your Friends Close and Your Guest List Closer: “If you really want to keep it secret, you have to invite fewer than 100 guests, and that is really pushing it. Second, like in the case of Jennifer Aniston, or Justin Timberlake and Jessica Biel, it helps if people have no idea where they are going. When we planned LeBron’s wedding, we sent an invitation that said it was going to take place somewhere on the West Coast, but we didn’t give details until we called them back, after we vetted them to make sure it was an invited guest or their representative. Still, it’s rarely foolproof. One of their save-the-dates showed up on TMZ.” — Marcy Blum, Marcy Blum Associates, New York.

Secure the Perimeter: “The problem is, once something leaks to one press outlet, it’s like sharks feeding on a dead carcass. They swarm. I did a wedding a few years back in the Hamptons involving some very well-known artists in the music industry, and we had security every seven feet around the perimeter of the property. The media will sit outside, waiting for leaks. And they don’t just show up the day of. They’ll be talking to people who provide luxury trailers, the generators, it could be the tenting company. We have to plant security four or five days in advance.” — Andrea Correale, Elegant Affairs Caterers, New York.

Establish a Paper Trail: “Very often in an event of this magnitude, you have two to three hundred people on site. It’s not just the caterers you have to worry about. There are lots of vendors involved: musicians, people renting lounge furniture, fabric people. You have to make sure you get the proper forms signed so no one in the other companies leaks word, either. You dot your I’s and cross your T’s, but in the end of the day, you can’t control everything.” — Andrea Correale.

Spare the Phones, Spoil the Party: “Unless you’re going to make every single guest including Cousin Harry sign a nondisclosure agreement, then nothing is foolproof. So we leave a letter in the guest rooms saying: ‘We really want you to be present for this. Please don’t bring a cellphone, if you do bring it we’re going to ask you to leave it at the check-in desk.’ Then we organize them and put them in separate plastic bags with the number on the outside. It’s not about the couple being so paranoid. There are a lot of non-famous people there. It could be a cousin, an old college roommate. It’s about the couple not wanting the famous guests to be bothered by the non-famous guests for selfies. It’s a wedding, not a red carpet event.” — Marcy Blum.

No One Is Above the Law: “With guests, you can say ‘Please don’t take pictures,’ but you know they’re going to Instagram it, so we have just said, ‘Please deposit your phones.’ You can ask them to shut them off, but they won’t. Some people take great umbrage and don’t want to give up their phones. There was a celebrity once who told me, ‘Hey, I’m not going to do it.’ We just had to watch that person. You can always tell what they’re doing. If someone takes a picture just to take a picture, they put the phone down. But if they take a shot and start typing simultaneously, they’re leaking it out.” — JoAnn Gregoli.

Consider Calling in the Air Force: “Really only in the last year, these magazines are buying drones. They are able to launch them, hover them low. You could drop a drone outfitted with video cameras into a property almost undetected. At one event I did recently in the Hamptons, one came in over the water. There is no way we could have stopped it. They are a lot more annoying than helicopters ever were. Before, with a helicopter, you had a TV crew on board, and you’d have to wait for the show to air. Now with drones, they can put it on YouTube, on Periscope, on Twitter, almost in real time. To the world of celebrities, that is horrible. What do you do: Shoot them down?” — JoAnn Gregoli.