The Swiss are record-breaking rail travellers, spending more time in trains than even the Japanese. A dense network of often improbable lines wraps around and perforates the country’s many high mountains, sewing 26 disparate cantons into a single nation.

Upon its 1882 opening, the Gotthard line – through extremely challenging terrain and using spiral tunnels, long galleried sections and dozens of bridges – was celebrated as a marvel of engineering. It climbed to a 15km summit tunnel, then the longest of its kind anywhere in the world.

The line was regarded as essential to the Swiss economy, ensuring that trade flowed through the country rather than around it. But in the route’s first year of operation, a million passengers came for the views of giddying drops, of steep mountainsides dotted with cattle, and of hidden valleys not even served by footpaths.

Now, the opening of a 57km tunnel through the base of the Saint-Gotthard Massif has reclaimed for the Swiss the title of world’s longest rail-tunnel builders. More impor­tantly, it has freed capacity on the original route for the newly inaugurated Gotthard Panorama Express, the wrap­around win­dows of which offer views of CinemaScope scale.

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The experience begins not on rails but afloat, on one of the century-old paddle steamers that departs from docks conve­niently close to Lucerne city’s station. The vessel waddles in a stately fashion from one end of Lake Lucerne to the other, zig-zagging between tiny towns of sharply spired churches and solid-looking wooden houses on narrow stretches of flat land that are dwarfed by the surrounding mountains.

This banquet of scenery can be comple­mented with a fabulous three-course meal in the steamer’s beautifully restored dining room, which is all wood panelling, mirrors and potted palms.

By contrast, the smartly red-and-white-liveried Gotthard Panorama Express that waits close to the steamer dock at Flüelen is a picture of modernity.

It has barely begun its long climb when a menu appears, offering prosecco and wines from the Italian-speaking Ticino region of Switzerland, which is the train’s destination, along with assorted southern delicacies and coffee with grappa.

The route winds along steep-sided valleys, where chapels with ornate towers are perched on promontories, as if overseeing small, steeply sloping pastures. The line makes a double loop to gain height, passing the baroque Wassen Church three times and drawing passengers to the photo coach (which is simply an old-fashioned carriage with windows that can be wound halfway down).

The train slows for the summit tunnel, where the history of its construction is projected on the walls. The line then carves underground circles, reappearing below where it entered on the mountainside, and squeezes past compact vineyards and great stacks of firewood ready for winter, some­times passing beneath modern highways that soar by on concrete stilts.

The train continues to the city of Lugano, but alighting at Italianate Bellinzona gives the opportunity to complete a grand tour of panoramic trains back to Lucerne, first riding a comfortable bus northeast for a night in pretty Chur, Switzerland’s oldest city.

There’s time in the morning to admire the largely medieval town centre and to explore a street plan laid down by the Romans before boarding the Glacier Express, which passes through en route from St Moritz to Zermatt. First advertised in the 1930s as “the slowest express train in the world”, it crosses the route of the Gotthard as it heads west, offering similar panoramic cars, a kitchen with wine cellar and conventional carriages for Swiss simply getting from A to B.

The panorama cars each have a rack at the entrance for coats, polite and efficient table service, and the atmosphere is altogether more of a restaurant on wheels than a train, with every table a window table.

A small chime indicates when commentary on some landmark or other is about to be broadcast through earphones. But if you are not interested in geology, or the number of species of local butterfly (350, apparently), the option here is simply to drink in the scenery undisturbed, perhaps while enjoying a three-course meal freshly prepared – and wrapping up with Swiss chocolate cake – on the train itself.

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As with other mountain lines, the route is mostly single-track with passing opportu­nities at the stations of mountain towns. At one point, the engine is exchanged for one with cogwheels, to drag the carriages up steep inclines to the 2,033-metre Oberalp Pass, and to hold them back on the equally steep descent to the resort town of Andermatt, which becomes visible far below long before it is reached. Glaciers wink from atop distant peaks and castles guard valley entrances as the train threads through the slender gorge of the newly born Rhine.

Alighting at the town of Brig makes possible a connection to French-speaking Montreux at the eastern end of Lake Geneva, with its unexpectedly Mediterranean atmosphere, which attracted 19th-century literary greats such as Lord Byron and Percy Bysshe Shelley, and 20th-century rock stars David Bowie and Freddie Mercury. There are famous casinos, or the opportunity of a lake­side promenade to the labyrinthine Château de Chillon, most of which dates to the 13th century.

In the 1920s, three train companies linked their schedules to create the GoldenPass route from Montreux that skirts several lakes and crosses multiple passes. These days, what’s known as the Belle Époque version of the train features elegant recreations of carriages from the 30s, with wooden panelling, brass fittings and antimacassars on embroidered seats.

Once the longest electrified narrow gauge railway in the world, this remains the steep­est line in Switzerland without cogwheel assistance. The train climbs painstakingly out of Montreux and offers views across Lake Geneva before winding into the mountains, past churches with spires like wizards’ hats and massive dark-wood farmhouses built on proceeds from cattle breeding, before eventually winding back down to Lucerne.

The Swiss may now hurtle through the Gotthard Base Tunnel at up to 250km/h, but relax. Let them take the low road and arrive before you.

“Waiter? Another prosecco, please.”