It’s difficult to resist the temptation to wander the battlements wringing your hands. Or declaiming something along the lines of “When sorrows come, they come not single spies, but in battalions.” Back in the late 16th century, Kronborg Castle wasn’t really anything grander than a maritime toll station, extorting taxes from shipping heading into the Oresund channel. Then, it just happened that some Stratford scribbler was looking for an exotic location for his latest play and liked the three-syllable poetry in the name of the castle’s location.

Hamlet put Elsinore, or Helsingor as the Danes know it, on the literary map, but the castle seems anything but romantic. Sturdy, austere and wind-blasted, it still looms threateningly over the water, even if the cannons are now ornamental rather than directed at potential Swedish invaders.

A young, blond Larry Olivier gave the Danes his Hamlet there in 1937, with Vivien Leigh his Ophelia, and in summer it is still the venue for theatrical productions, even if its exposed site is less than conducive to sensitive thespian artistry.

Kronborg’s grim facade is something of a bluff, though, because lurking behind the fortress is some of Europe’s most welcoming countryside. There’s not much rotten in this particular state of Denmark. North Zealand is a lush and comfortable region, a place where Copenhagen commuters can kid themselves that they are traditional rural Danes surrounded by the lapping of the waves and the lowing of the cattle.

The closest you find to a town of substance in North Zealand, Helsingor isn’t really typical of the region and can present a slightly alarming spectacle on first appearance. The main shopping drag, Stengade, seems to harbour a disconcerting number of alcohol outlets. For every sober bookshop or butcher’s, there is a garish wine warehouse or mini-market touting slabs of lager on special offer.

The reason is one of those anomalies that make the European Union such a bureaucratic delight. Twenty minutes across the water in Sweden, Denmark’s hapless neighbours have to deal with the sort of prohibitive taxes on booze that make it necessary to take out a second mortgage to buy a decent bottle of chablis. Denmark is more enlightened, and substantially cheaper, which means the regular ferry crossing back over the Oresund to Helsingborg in Sweden carries more liquor than a Govan housewarming.

Resist the temptation to get hammered at knockdown prices, and Helsingor offers a few more salubrious attractions. The medieval quarter has a modest cathedral and a well-preserved Carmelite monastery.

Jostling for your attention amid the alcoholic cornucopia is a hidden treasure, Ole Jensen’s cheese shop. This carries more aromatic variants of the ripe dairy products than I have seen anywhere outside the cheese-crazy town of Alkmaar in Holland. It is more redolent of the real Zealand, a land where cattle graze in the succulent grass and every small farm makes its own cheese.

There’s a slightly wilder feel along Zealand’s north coast, especially outside the summer months, when the small towns are thronged with Copenhageners enjoying the sun or windsurfers chasing the breezes. In Hornbaek, a short train ride up the coast from Helsingor, the soft white sands could be Caribbean were it not for the brisk temperatures. A medieval atmosphere still prevails with tidily thatched houses, timbered taverns and a lovingly preserved prettiness.

Gilleleje, Zealand’s most northerly point, is a little rawer, a fishing port where maritime business is still more important than tourism. Here is the place to eat the local smoked mackerel, wash it down with a fresh and bracing aquavit, and enjoy the experience of being on the very point of Denmark that always looks like it is about to be chewed up by the descending maw of Norway and Sweden.

Westwards lies the soporific, dune-protected seaside village of Tisvildeleje, which reminded me of Fife, only cleaner. There are walking paths through wind-blasted forests and heather-covered fields and Scotland seems very close here.

On the train line inland, Hillerod is the location for Frederiksborg Castle, which is far more like the romantic conception of a dramatic castle in Denmark than Elsinore. Spreading comfortably across three islands, the predominantly 17th- century folly has a film-set interior with the sort of impressively tasteless splendour that typifies royalty, whatever their nationality.

Frederiksborg is the perfect end to a day that began by the coast on the Elsinore battlements, the surroundings worthy of any prince of Denmark. You can stand in the Knight’s Hall with all its regal trappings, and the mind can’t help but turn to the pressing matter of whether to bump off your dastardly uncle. Don’t start mumbling on about “rich gifts wax poor when givers prove unkind” too loudly, though, or the tourists will think you’re a lunatic — and that never has a happy ending.

Details: BMI (www.flybmi.com) has direct flights to Copenhagen from Edinburgh from £214.10 return or Glasgow from £216.20.

Helsingor is 45 minutes by train from Copenhagen’s central station (www.rejseplan.dk for timetables). The line continues to Hornbaek and Gilleleje.

In Helsingor, Marienlyst hotel and casino (00 45 4921 4000, e-mail: hotel@marienlyst.dk, www.marienlyst.dk) has doubles from £112. In Hornbaek, the stylish Hotel Hornbaekhus (00 45 4970 0169, e-mail: info@hornbaekhus.com) has doubles from £119.

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