Some nightspots suit jazz; others were born to boogie. In the Ambassador’s Lounge it has to be mambo. Only music as brassy and unmistakably fifties as the club itself could hope to match its Technicolor boldness: here, cherry pink and apple blossom white meet ocean blue and hot tomato red. In truth, I had a particular tune in mind. There’s something about the carefree musicality and Cuban-American sassiness of Xavier Cugat’s Siboney that’s perfect for this luxurious fifties time capsule.

To enjoy it, however, you must travel to Rotterdam, not Havana. To the city’s floating namesake: SS Rotterdam. The fifth (and not the last) Dutch liner to bear the name, she is without question the most illustrious. Built in the late fifties just as the transatlantic trade’s post-war boom began to falter in the face of competition from the Boeing 707, she was dubbed tomorrow’s ship, today. No-one could then have imagined how much truth there was in that brave claim, for in the decades that followed the flexibility of her layout, her engines-aft configuration and retro-futuristic silhouette became the blueprint for a new generation of cruise ships. In one breathtakingly sleek package she was one of the last great North Atlantic liners and one of the first truly convincing cruise ships.

At 38,000 tons and 750ft in length, the Rotterdam is not large by the standards of today’s Miami-based behemoths, but in 1959 she was among the larger liners plying the Europe to New York route, and the largest ever built in Holland. With size came dignity: as the flagship of the Holland-America line, she was – like Cunard’s Queens – a true ship of state, the flagship of the Dutch merchant marine and a vessel for national prestige as much as a means of transport from the old world to the new. She was launched by Queen Juliana; her elegant Ritz Carlton ballroom hosted Prince Rainier and Princess Grace of Monaco. Frank Sinatra performed in her theatre. That’s the kind of glamour today’s Cancun-bound resort ships have a hard time living up to.

She has the looks to match – looks that subsequent generations of passenger ships have gradually lost. In the first two decades after the Second World War naval architecture reached an apogee of grace, as streamlined modernity met the minimalizing impact of improved technology on ships’ silhouettes. Funnels were reduced in number and the old-fashioned clutter of ventilators and masts was swept away to be replaced by open-air swimming pools, terraced open spaces and clean lines. Among the first examples of this new style were Italian ships like the ill-fated Andrea Doria of 1951; among the last was the QE2 of 1968. The Rotterdam arrived midway through this golden age, and her elegance of line – from curved stem to cruiser stern – disguises her considerable size. She has the look of a yacht about her.

After an illustrious career, she managed somehow to avoid a one-way trip to the beach at Alang in India, where old ships go to die. Rotterdam returned to a tumultuous welcome in her home port in 2008. She was then stripped to the bare metal for a thoroughgoing restoration that was complicated by the liberal quantities of asbestos used in her construction. The Rotterdam reopened as a static hotel ship and museum in 2010, but even then all was not plain sailing: the cost of restoring her overwhelmed her rescuers and for a time it was rumoured that she might depart for an uncertain future in Oman.

Happily, it didn’t come to that. New owners were found, and I spent a bleak midwinter night on board in the dying days of 2012.

A Christmas tree and a flaming brazier cheered the blustery quayside; a liveried footman warmed the welcome aboard. Beautiful as she is on the outside, it’s Rotterdam’s interiors that are the most evocative thing about her. The ship’s hot 1950s colours made a delightful antidote to the grey December drizzle and a refreshing change from the timid whites and beiges of contemporary good taste. At once grand and intimate, she’s big enough to have a 600-seat theatre yet small enough to retain inside the yacht-like ambience her elegant hull suggests. An Atlantic crossing to or from New York in her late fifties heyday must have felt less like a stay in a grand hotel than a glamorous four-day house party. On the North Atlantic in the fifties the classes were still divided, but on Rotterdam the division between the VIPs in first class and the tourists in second was a discreet one, removed entirely when she cruised.

What makes this lovely ocean liner so special is not just her once-revolutionary design, but that she has survived in such original condition. She is as perfect a period piece as a pink Cadillac, a Douglas Sirk movie or the sexual chemistry between Doris Day and Rock Hudson. This is the fifties as experienced by affluent Americans, and there are luxurious touches everywhere: deep, cossetting armchairs so heavy it’s a struggle to move them, a bronze dance floor patterned in imitation of the sea bed, mosaic table tops fashioned from Murano glass and – above all – wonderful modern art, from sculpture to painting and tapestry. Though the crew-to-passenger ratio is not at all what it was in her North Atlantic heyday, she makes a surprisingly successful hotel. I had an immaculate, spacious cabin in the former first class section of the ship. Its décor was a nice mix of boutique hotel modern and fifties retro, with original, custom-built cabinets and a fifties magazine on the coffee table.

By day you can tour the ship from bridge to engine room with an audioguide, though for the latter you have to join a group. Former crew members are on hand to explain the workings of the bridge or simply to tell anecdotes of their years at sea. But daytime wanderings can be thwarted by the conferences and wedding receptions that ensure the ship’s public rooms earn their keep. There are no such bars to exploration for an overnight guest, and I seized my chance to see the magnificent smoking room, Ritz-Carlton room and Ambassador’s Lounge in complete solitude, with only my camera for company.

After dinner I nursed a cocktail beneath the fish-scale ceiling of the ocean-themed bar, coveting Aart van de Ijssel’s extraordinarily prickly red copper wall sculpture, which resembles nothing so much as an attenuated, cupric plateau de fruits de mer. The drink was good and strong; the music suited the setting. There was no mambo, but one by one the voices of Ella, Frank and Tony gave aural expression to the atmosphere of fifties luxe. As on any good sea voyage, there was no particular rush to do anything. So I lingered awhile, content and just a tiny bit drunk, waiting for Doris Day.

SS Rotterdam, 3e Katendrechtsehoofd 25, 3072 AM Rotterdam, Netherlands. Tel : (+31) 10 297 30 90
http://www.ssrotterdam.nl/uk/
Xavier Cugat’s 1950s recording of Siboney on YouTube: