“Oh my gosh, there they are!” whispers Innocent, my guide. I see the flick of a long tail through the tall, yellow-tipped grass. Ahead of us sit the two cheetahs we’ve been tracking for the most of the morning in western Zambia’s Liuwa Plain National Park. The big cat slinks forward, her 8-month-old cub following in a playful zig-zag. In the distance, we see two oribis (small antelopes) skipping ahead.

The cheetah’s ears perk up, so we follow her.

We’re the only vehicle watching. March through June is meant to be high season, but there are no engines roaring, no khaki-clad tourists hanging out windows of Land Rovers. On safari, this is rare. Most sightings are shared with others — but not in this faraway park on Angola’s border.

To get there, you have fly to Johannesburg (17 hours from JFK, from $1,150 roundtrip), then onto to the Zambian capital of Lusaka (a two-hour journey, from $430 roundtrip). Then comes a smaller plane (for 2½ hours, from $880 roundtrip) to Kalabo, on the outskirts of the park, and a helicopter to the lodge, the six-villa Time + Tide King Lewanika (from $1,320 per person, per night).

Opened last year, it’s Liuwa Plain’s first permanent lodge, making the park that much more attainable. One-percenter couples and adventurous families come for the lack of tourists and intimate encounters with wildlife.

Designed by renowned African design duo Silvio Rech and Leslie Carsten — of North Island in the Seychelles, where Prince William and the Duchess of Cambridge honeymooned — it also looks good. Their other new project is a 2017-opened beach retreat called Time + Tide Miavana (from $3,000 per person, per night).

It similarly rendered an obscure part of the world reachable. Located on the tiny Nosy Ankao island, off the northeastern tip of Madagascar, there is a three-hour flight from Johannesburg to the island — once a week (from $981 roundtrip). “Guests can literally dive reefs that have never before been explored,” says Darren Humphreys, of tour operator Travel Sommelier, which offers a 10-night all-inclusive trip to both resorts for $24,995 per person.

Time + Tide Miavana’s 14 villas have private pools, outdoor showers and sunken bathtubs with views of endless creamy beaches and turquoise Indian Ocean waters. Activities like stand-up paddleboarding, snorkeling, fly-fishing and dolphin-watching will keep the whole family busy.

Back in Liuwa Plain National Park, the oribis have skipped away. Seconds later, the cub starts chasing a small hare. Finally, it pounces on its prey. It’s wild, undiscovered and perfect.

The author was a guest of the resorts.