It’s that magical moment between day and night, when the sun puts on an awe-inspiring encore while the inky darkness of night swallows up its stage. Far below, another performance is being enjoyed by guests of a sleek superyacht; a pod of inquisitive humpback whales ring the vessel, slapping their flukes against the shimmering water and filling the air with honey-hued mist as they prepare for their next dive. Not content with simply watching this placental performance from the decks, we bundle up and take to the water in a fleet of military-grade zodiacs for a mesmerising up-close-and-personal Antarctic encounter the likes of which few have experienced.

However, it’s an encounter that an increasing number of ultra-wealthy travellers are seeking, as they soar over conventional destinations like Monaco and Tahiti in their private jets, en route to the world’s farthest flung corners, where a small fleet of expedition-ready superyachts offer creature comforts and unforgettable memories in equal measure. The global superyacht charter market is growing in leaps and bounds. But not all charter vessels are created equal; destinations like Antarctica, the Arctic, Melanesia and North Asia require specialist vessels with ice-strengthened hulls, sophisticated navigation systems, and the kinds of built-in redundancies that will have you thanking your lucky stars if things go awry thousands of kilometres from help.

We’re cruising the Antarctic Peninsula aboard the beautiful Hanse Explorer, one of the custom-built yachts used by specialist superyacht charter gurus EYOS Expeditions. A ground-breaking charter business founded by Tim Soper and Rob McCallum, and operated by a clutch of hardy-yet-passionate travellers, including experienced marine officer-turned-CEO Ben Lyons, EYOS will take you, your friends, and your superyacht (if you’re fortunate enough to have one) to almost anywhere on the planet you so desire.

“The polar regions are clearly the ‘hot’ destination now for expedition yachts and we’re seeing more and more yachts venturing into more distant itineraries,” says Lyons as he guides our zodiac. “People that travel with us on expeditions want to see, learn and do more. They’re interested in where they’re going and they have a different view of what luxury and privilege mean. To them, luxury isn’t getting into the top restaurant in St Barths – it’s about going somewhere nobody else can get to.”

If you don’t count a superyacht among your most prized possessions (or don’t fancy scraping the paintwork of your palace at sea) EYOS also offers access to a myriad of world-class expedition-ready charter yachts, like the Hanse Explorer, priced up to US$1 million a week. In addition to the charter, EYOS supply a hand-selected team of experienced expeditionary crew and guides, offering the perfect marriage of luxury and logistics.

“The trend towards expedition yachting mirrors the explosive growth in the expedition cruise industry,” says Lyons. “We see a real interest in yacht clients wanting to go beyond the Caribbean and Mediterranean. Seven years ago, there might have only been one yacht in Antarctica for charter. This season, we’ll be working with six private yachts, all but one of which are available for charter. In the Arctic, we see the same thing.”

A key component in this growth is the ability to now fly over rather than battle your way through the dreaded Drake Passage, a tumultuous strait between Antarctica and South America that’s often regarded as the most violent on the planet, landing by charter flight at King George Island, on the cusp of the Antarctic Peninsula. Leave the mainland after breakfast and you can be cruising the likes of the infamously ice-choked Antarctic Sound by lunch.

The Sound, our first stop, is a thrilling landscape rarely visited by the larger commercial vessels, which ply the west coast of the Peninsula on regular but inflexible itineraries. Among the towering icebergs of the Peninsula’s northeastern tip is where our agile vessel comes into her own. With her navy-blue hull and sleek, rakish lines, the Hanse Explorer is one of EYOS’ most popular charter yachts and wouldn’t look out of place in a Mediterranean marina. But beneath the Ferrari-like aesthetics lie cutting-edge environmental systems, the highest rating for an ice strengthened hull, powerful engines, and a 9,000nm cruising range. In addition, she accommodates 12 guests in spacious en suite staterooms, and boasts sublime lounges and dining rooms, open sun decks, and an experienced hotel crew who cater to every guest’s whims.

A few days into our week-long adventure, I rise just before dawn– or at least the transition between the shades of twilight that represents the birth of a new day this close to the South Pole – and join captain Jens Köthen, a perpetually cheerful German with the effortless grace of a luxury hotel manager, on the bridge. The Hanse Explorer has an open bridge policy, offering guests a unique perspective on the challenges of Antarctic navigation. The horizon, a silver line that seems to drift in and out of sight as if in a dream, is gradually broken by great slabs of ice the size of city blocks, each emerging from the morning mist like the vanguard of an approaching horde.

Each evening, over canapes in the saloon, expedition leader Richard White, an adventure veteran, outlines the plans for the day ahead, but there is an inherent flexibility sewn like gold threads into the best laid plans because there’s no telling what mother nature might offer. See something you like? Land on a beach where you just might be the first human visitor. Crave new found friends? Arrange a visit to a remote scientific base. Greeted by pods of orca in Niko Harbour? Launch the zodiacs! Even shy Portuguese chef Luis Galego Pião follows the mantra “the destination comes first”, and the Baked Alaska be dammed.

“Private charters mean freedom for a select few,” says White, who, during one such outing, expertly guides our zodiac through narrow channels between towering cliffs, Arctic Terns dipping and darting high above. “These are people who are well off and want to use their money to discover the wonders of the world, and we’re only too happy to take them there.”

Each day offers a new adventure, a new discovery. In Antarctic Sound, we cruise through great sea caves and brave ocean swells before beaching at Brown Bluff where, in the shadows of snow dusted cliffs, ranks of ice cathedrals, some blindingly white, others majestically blue, litter the bay. In Mikkelsen Harbour we’re welcomed by roaring fur seals, oblivious Adélie penguins, and the weathered wrecks of timber long boats dating from the region’s bloody whaling history; and to the south, in the Grandidier Channel, farther than commercial vessels dare to tread, we discover great sways of sea ice floes, which jostle for space with icebergs that rival Notre Dame in size and intricacy. After slicing and ploughing our way through the ice, the captain positions the bow against a tennis court-sized floe, offering us the perfect Antarctica photo op as the snowfall clears and the sun baths the shimmering landscape in gold.

Although Antarctica is the most popular, many other destinations are seducing adventurous superyacht travellers. “Papua New Guinea in particular has become a key destination,” says Lyons. “There’s intact culture, excellent diving and WWII history. It is an anthropologist’s dream.” He also counts the Solomon Islands, Vanuatu, and Indonesia’s Raja Ampat as emerging locales, but for us, the magic is here in Antarctica, where the heavens meet the ice, and where the crowds of city life are a distant memory.

Charter the Hanse Explorer from €200,000 (US$236,600) ++ per week, from EYOS Expeditions.