I had never imagined the Eucharist in German would be so easy to understand. "Das ist mein Blut..." said the Archbishop of Liechtenstein as he continued his liturgies from the open marquee. Meanwhile, I wondered what I was doing at 9.30am, in heavy rain, sheltering under some dripping alders in the fourth-smallest country in Europe.

It was 15 August 2008, and I had left my pension in the Austrian border-town of Feldkirch early, so as not to miss the start of Liechtenstein's National Day celebrations. The bus into Vaduz, the capital, took 35 minutes – and from the bus stop, I had made my way up to a field next to the Schloss Vaduz, the "Princely" Residence, perched on a bluff looming over the town.

The castle grounds are open to the public only once a year, on this date, when Crown Prince Hans-Adam II generously offers free drink and food to the entire population. Out of a possible 35,000, only a couple of hundred had braved the weather for mass – perhaps surprising in such a Catholic country – although more showed up later at the Schloss for freebies.

After prayers, Hereditary Prince Alois stepped up to the podium. Prince Hans-Adam transferred sovereign rights to his eldest son in 2004, making Alois – married to Duchess Sophie of Bavaria – his representative in all acts of state. Alois is set to become the 16th Crown Prince in 400 years in the Principality of Liechtenstein, 62 square miles sandwiched between one bank of the Rhine and the towering Three Sisters massif.

The man standing next to me sensed I didn't speak German and translated parts of the stork-like Prince's speech. Alois apparently reassured his citizens that the country would weather the economic crisis, and that unfavourable media coverage of its banking secrecy would not discourage trade. I remembered the slogan I had read on a brochure in the tourist office: "Transparency where necessary, privacy where possible." The gentleman I was talking to had come over from Berne for the day and was a diplomat from North Korea.

When Alois had finished, a band struck up a national anthem that proved easy enough to mumble along to, as it's sung to the same tune as "God Save the Queen" (Long live Liechtenstein happy and true on the youthful Rhine, Long live our country's prince, Long live our fatherland, and so on), one startling difference being that on the high notes, everybody snaps-to with a half-arm open salute. We then filed up the hill and into the walled castle garden. The whole area was festooned with bunting in the royal blue-red pattern; even the bread rolls were emblazoned with the coronet of the Princely House. In between mouthfuls of giant salty pretzels and beer, I actually had the opportunity to thank Prince Hans-Adam in person for his generosity.

Down on the streets of Vaduz, the Landesmuseum, sepulchral Art Museum and Postage Stamp Museum are as modest as you might expect for national institutions in a postage-stamp-sized country. I got my passport franked in the tourist office, where the staff recommended a hike for the next day. In the evening, I ate traditional käsknöpfle – cheese dumplings topped with onions. According to the brochure, Liechtensteiners are "not averse to gourmet dining", and there are in fact two Michelin-starred restaurants in the country.

Liechtenstein has no state debt, and negligible unemployment. Such factors have attracted institutions as diverse as the John S Latsis Public Benefit Foundation, the Hoval Group – who provide the central heating for Buckingham Palace – and Ivoclar Vivadent, the world's biggest manufacturer of false teeth. Presumably, it is companies such as these that lend Vaduz the aura of cosmopolitan slickness so surprising for an Alpine outpost.

The weather had half-cleared the next morning so I took a bus up to Triesenberg, and then Gaflei – the starting point for the dramatic Fürstensteig Trail, which wends its way through the clouds above the Rhine valley at 2,000 metres. Liechtenstein is stunningly beautiful, with great skiing in the winter around Malbun, or the 250 miles of summer biking and walking paths in the majestic Oberland. Being Liechtenstein, the hiking trails are immaculately tended and well-signed, and all are easily reachable via the space-age bus network.

After a couple of hours, my hike got too dangerous as the mist started to come in, but the views were well worth the prayers in the rain, and even those cheese dumplings.

Liechtenstein Tourism: 00 423 239 63 00 tourismus.li