When we were living near Cusco, my children showed a marked disinclination to join me on any of the research trips I was taking to the coast or Nazca: "why go and see some boring old lines in the desert?" was the usual reaction. But the prospect of going to Puno and the Island of the Sun by train did excite them, both because it sounded tantalisingly exotic and warm – and because it is no ordinary train.
For the about the price of a single ticket from London to Birmingham, you can take one of the most luxurious and exotic railway trips in the world. PeruRail has kitted the Cusco-Puno line out with all the luxury of the Pullman trains of the 1920s: traditional coaches, panelled woodwork, an observation car, linen tablecloths and full dinner service. The detail that the children most enjoyed was that rather than having fixed seats, the club armchairs can be moved around as you travel – although after a few hours' experimentation both the carpet and our patience started to wear thin.
There used to be a "Backpackers" carriage, but now the only option is to pay $134 (£70) for a one-way, first-class ticket. This includes a three-course lunch; somehow food tastes better when looking out at the bleak altiplano. It also allows use of the glass-walled observation car, where you can sip a cappuccino or coca tea as you take in the stupendous views.
This is a journey that takes you through what is sometimes called "a sacred landscape", the Inca heartland that connected the two places most important to their world: the capital, Cusco, and the holy shrine of the Island of the Sun on Lake Titicaca, from where legend holds that they originated.
It took 35 years for the line to be laid, due to intervening wars, economic crises and the ambitious engineering required, before it was finished in 1908; this year sees its centenary.
The train climbs from the already considerable altitude of Cusco at 3,600m to the midway high-point of La Raya at 4,321m; there's a stop here for passengers to disembark, stretch their legs, shop for locally made alpaca goods and feel fatigued from even this small exertion at altitude.
Along the way it passes Rumicolca, the great stone gateway which marks the southern approach to Cusco; and the ruins at Raqchi, one of the earliest and most unusual Inca sites, with towering walls built from both adobe and stone.
The altiplano's austere beauty then stretches ahead - too high for most crops, but herds of llamas and alpacas still graze at these altitudes. After passing La Raya you descend to the very edge of Lake Titicaca where a particularly beautiful stretch of line by the lake shore takes you on to Puno.
If you plan to return to Cusco, the smart way to make the reverse journey is with one of the excellent bus services that stops at some of the sites like Raqchi along the route.
This full-day treat made up for my children's disappointment at the Island of the Sun. While it is a superb destination, it is not named for its heat. Instead, Inca myth insists that the sun – and indeed their race – emerged from a rock on the island. While a beautiful place, at 4,000m-plus, it felt distinctly chilly.
The train runs in each direction on Mondays, Wednesdays and Saturdays. It is scheduled to leave at 8am, arriving around 10 hours later. More information: www.perurail.com
The Inca Express bus service stops at sites on way to and from Puno. The fare of $34 includes in-bus refreshments and lunch, but not admission to attractions; see www.inkaexpress.com