We travelled more than 4,800km from the Arctic Circle to the Atlantic Ocean in nine days, visiting six countries. We saw nine museums, sang on a live television show, went on three walking tours and lingered over glasses of red wine while hurtling past grassy hills in the moonlight.

And once we started our trip, we never stood in an airport security line. We did it all using Europe's exemplary train system.

The excursion was inspired by a 2011 rail adventure. After travelling to Istanbul for work, Susan, a university professor, celebrated a professional milestone by taking trains west to Paris. We initially thought of redoing that trip from the opposite direction, but decided a less familiar route might be more fun. If not Europe from west to east, how about Europe from north to south?

Consulting rail maps, we decided to start about 145km above the Arctic Circle, in Kiruna, the northernmost town in Sweden with regular passenger service. Where to conclude? We considered various southern European destinations but settled on Lisbon, Portugal.

The pleasure, we decided, would be in the process. We would think of trains not as mere modes of transit, but as relaxing destinations in themselves. During our stops - in Stockholm; Copenhagen, Denmark; Cologne, Germany; Paris; Barcelona, Spain, and Madrid - we would resist the urge to hit every tourist destination. But in each city we would take in culture and eat or drink something typical.

We landed at Kiruna's tiny airport on a Sunday afternoon. Beginning our travels then made perfect sense - until we learnt that we had missed, by a day, Kirunafestivalen, a three-day event that attracted pop acts known throughout Europe. Ah, there was a reason that a city of 23,000 felt as if nearly everyone had just left. It was true.

By mid afternoon, we were at the Kiruna station, waiting for the train to Stockholm, eager to meet the strangers we would sleep with that night.

We had hoped to book a private, two-bunk compartment for the 16-hour trip, but by the time we made our travel arrangements, those accommodations were sold out. So we had selected two bunks in a couchette.

The compartment had six seats, which converted to padded bunks. We and our travel companions - an Austrian couple who appeared to be in their 60s and two Swedish college students who had been camping at the music festival - each received two clean sheets, a blanket, a pillow and drinking water.

For the next eight hours, we enjoyed the passing landscape, chatted, read and made trips to the cafe car, which served drinks, snacks and simple meals.

The Austrians, the first to turn in, converted the seats. So by the time we finished a last glass of wine as the cafe car closed at 11pm - with the sun still well above the horizon - all we had to do was climb into our top bunks.

No one snored too loudly, and we wished our travel companions good journeys as we parted in Stockholm at breakfast time. Our hotel room was ready immediately, so we were able to get a shower before heading to Djurgarden Island to lunch on smorgas, open-faced salmon and shrimp-salad sandwiches, and tour the Vasa Museum.

There, we spent hours marvelling at a wooden ship retrieved from Stockholm's harbour in 1961, more than 300 years after it sank on its first voyage.

When John headed to the Abba Museum - dedicated to the 1970s pop music of Agnetha Faltskog, Bjorn Ulvaeus, Benny Andersson and Anni-Frid Lyngstad - Susan chose a walk around the island and found herself at the entrance to Skansen, a park sheltering historic buildings from throughout Sweden.

The ticket-seller said that admission included "a concert", which turned out to be Allsang Pa Skansen, an hour-long variety show that takes place every summer Tuesday and has been broadcast live since 1979. John caught up to watch some of the musicians we had missed in Kiruna, including Tomas Ledin, a singer-songwriter whose career is well into its fifth decade.

We heard girls and their mums scream for 29-year-old singer Mans Zelmerlow as he performed Heroes, the number with which he had just won the annual Eurovision Song Contest. We bought the Allsang songbook and sang along enthusiastically and phonetically to a tune called Trettifyran, which we learnt was a Swedish version of This Ole House, recorded by Rosemary Clooney in the 1950s.

The next morning, we continued south to Malmo and Copenhagen over the stunning, 16km Oresund Bridge - inspiration for the hit Swedish-Danish TV police drama The Bridge, which has spawned British-French and United States remakes.

In Copenhagen, we took a guided walking tour of the Christianshavn neighbourhood that ended at an alternative community, Christiania, and learnt that climbing 250 steps to the base of the spire of Our Saviour's Church would, for the next week, exact a toll on our hamstrings.

Over the next two days, we crossed from Rodby, Denmark, to Puttgarden, Germany, on one of the few European trains carried by a ferry; took a fast German InterCity Express to Cologne, where we viewed Roman ruins and drank kolsch; and rode a high-speed Thalys train to Paris, where we visited museums and had two lovely meals. One was lunch at La Bulle, an elegant and yet homey spot on Rue Louis Blanc in the 10th Arrondissement, where we had excellent ratatouille and lieu, a white fish.

We even did laundry at a French coin-operated lavarie before taking a TGV, or train a grande vitesse, to Barcelona for two nights. There, we ate tapas, attended Mass in the 12th-century church of Saint Anna, wandered through the Barri Gotic and took a walking tour of the architectural marvels of Antoni Gaudi.

For the final international leg of the trip, from Madrid to Lisbon, we boarded the Lusitania Trenhotel, operated by the Spanish rail company Renfe. We had reserved an ingeniously designed first-class, two-berth cabin with a sink. The Lusitania's cafe was open all night and we passed midnight there, sharing red wine and savouring the cheerful hum of conversations.

Such delights are dwindling. There is no longer a sleeper train between Paris and Madrid. Amsterdam has lost a direct overnight route to Warsaw, Poland. The Paris-to- Rome sleeper John took in July 2013 was discontinued the following winter.

One reason is that high-speed trains have eliminated the need for overnight travel on routes such as Paris to Zurich. And yet Mark Smith - whose website, the Man In Seat Sixty-One, is an indispensable guide to train travel - points out that there remain routes with no good daytime high-speed service, including Nice to Rome (more than eight hours) and Paris to Madrid (about nine hours).

Well-rested after our overnight trip from Madrid, we took a three-hour walking tour of Lisbon's older neighbourhoods. We then heeded our guide's advice to seek lunch in a nondescript place that seemed oblivious to tourists, and we found it in the Reviravolta, where we sat at a decidedly unglamorous formica table and devoured plates of expertly grilled sea bass and sardines.

But Lisbon was not quite our final stop, as it lies on the Tagus River.

To complete the journey, we rode a suburban train 45 minutes west to the beach town of Cascais, where a cab driver cheerfully agreed to take us 7km to Praia do Guincho, a rocky beach on the Atlantic Ocean. Gusts of 40 knots or more blew sand into our eyes as we made our way gingerly to the water. A windsurfer told us he was giving up for the day because the wind was too strong.

We touched our toes to the sea and then headed back to the waiting taxi. We had one more train trip to make, back to Lisbon. We looked out the windows on that final journey, satisfied that we had solved the conundrum of European travellers with limited vacation time: Is it better to cover a lot of ground or focus on relaxing?

Over nine days, watching from comfortable second-class seats as the countryside changed from birch forests to olive groves, we had done both.

NEW YORK TIMES