Why somewhere unfamiliar is riskier than your own back yard
Your dog knows the way home, even if you've never really thought about it. Over years of walks he's learned where to turn, which smell leads to your front door, and how the yard sounds first thing in the morning. Slip out near the flat, and he's got something to go on. On holiday that whole map is gone. The rented cottage by the lake smells foreign, the paths beside it lead nowhere he knows, and a dog who spooks once has no idea which way to run to get back.
With a cat it's much the same, maybe worse. A cat builds a precise plan of the ground in its head: where the hiding spots are, where its territory ends, which route it takes home. In a new flat none of that applies. All it takes is a slip through a window left ajar, and a few minutes later she's somewhere she doesn't recognise at all. There's no home to head back to, so instead of looking for one she hides and sits tight.
There's one more thing on top of that. Somewhere new, nobody knows your animal. At home a neighbour recognises the dog from the third floor and walks him to your door. At the seaside or on a campsite you're a stranger, and a found dog is, to everyone around, just a stray with no owner.
The holiday moments when a pet vanishes in seconds
Campsite, evening. Someone two tents over sets off bangers or fireworks, because they've got something to celebrate. Your dog, calm all day, suddenly wrenches free and bolts into the dark between the trees. In daylight he'd trace his own steps back, but at night, in a panic, in woods he doesn't know, he just runs straight ahead until he drops from exhaustion a few miles on.
The beach at the height of summer is the second place like that. Crowds, kids, other dogs, the smell of food from every side. You drop the lead for a second to spread the towel, and the dog's off after a gull or another four-legged one and lost among the parasols. On a packed beach twenty metres is all it takes for him to be out of sight.
Sometimes it's quieter and still ends in a search. You arrive at the family's place, open the gate, and the dog darts off down an unfamiliar street. Or you stop at a service station halfway through the drive, someone cracks the car door open, and the cat, who was only meant to catch her breath, leaps out somewhere two hundred kilometres from anything she knows. Each of these takes a moment, and the fallout drags on for days.
What to sort before you leave, so you sleep easier
The most important bit takes five minutes and you do it from the sofa before you pack the cases. Go into your account and check the details on your dog's profile are current. If you'll be reachable on a different number over the holiday, add it. If you're renting a place, you can put in the address where you're staying, so a finder knows the animal is a long way from home. The lovely part is that the tag stays exactly the same, and you only change what shows up once it's scanned. You don't buy a new tag for the trip.
Take a fresh photo too, ideally one where the outline and any distinguishing marks show up well. If the dog's mid-moult, or you've had the cat clipped at the groomer before you go, a photo from a year ago won't do much good in a listing. While you're at it, check the tag is sitting firmly on the collar, and that the collar or harness isn't already worn through. A frightened dog can pull free of loose gear with a single lunge.
For a longer trip or a crowd, a harness beats a collar on its own, since it's harder to wriggle out of. Check the buckles, the clips, and whether the tag isn't dangling off a worn ring. These are all things that hold for years at home without a murmur, and yet it's the unfamiliar place, at the worst moment, where they like to fail.
If they go missing anyway while you're away
If the worst happens, the rules are much like they are at home, you just have to square them with being on strange ground. Search the immediate area thoroughly first, because a frightened animal usually hides nearby and stays quiet. Then go into your account and mark your pet as missing, so anyone who scans the tag sees at once that you're looking for them.
Tell people on the spot: at the campsite reception, with whoever owns the cottage, in the local online groups and at the nearest vet. If they've gone missing abroad, write the listing in the local language too, even through the translator on your phone, because it's mainly locals who'll be looking. I've written out the whole plan for the first hours in a separate piece on what to do when a dog goes missing, and it's worth a calm read.