Doris the cat is looking at me with interest, her gaze a mixture of feline apprehension and flirtation that recognises me as a stranger bearing seafood. After a few seconds of contemplation, she winds herself around my legs, casually flicking her head upwards at the morsel in my hand. Niklas Nilsson, the fisherman to whose sister Doris belongs, lets out a laugh. "It isn't you," he says with a smile. "It's the crayfish she wants."
She's right to covet it. The crayfish I'm holding is any cat's dream, a pastel orangey-pink, with soft meat within. Doris emits a plaintive miaow. Not that she really needs my dinner. She has the fluffy, glossy-coated appearance of a moggy for whom crustaceans are in constant supply. Which, indeed, they are. Home for Doris is Vastra Bryggan, a small clutch of fishing huts and dwellings – you could barely describe it as a hamlet – on the southern edge of Sweden's North Koster island.
If that name doesn't sound familiar, there's no reason why it should. Hardly more than four square miles in combined area, the two Koster islands (North and South) are largely unknown beyond Scandinavia – tiny flecks on the Skagerrak strait, pinpricks hidden five miles out from Sweden's west coast, just below the border with Norway.
Yet, earlier this month, this diminutive pair of islets was given new significance. The Swedish king, Carl XVI Gustaf, dropped by, speeches were made, songs were sung, a ceremonial bell was rung and the area around the islands – 150 choppy square miles of sea – was inaugurated as Kosterhavet, the country's first marine national park.
Sweden has high hopes for Kosterhavet as scientific project and visitor magnet. Along with the Ytre Hvaler National Park, a similar enclave in adjacent Norwegian waters, it makes up a vast protected zone where a huge range of aquatic life flourishes.
This is partly thanks to unusual geological circumstances. Although the gap is narrow, the Koster islands are separated from the mainland by the Koster fjord – a deep groove that plunges to depths of 247 metres in parts, and has the chilly temperatures and rich salinity of open ocean. When such water rubs against the warm shallows of the shore, you have a fertile package. There are 6,000 marine species in Kosterhavet. Forests of kelp shimmer below the waves. Sea anemones twitch. Lophelia pertusa, a cold-water coral, sprouts in the darkness. Redfish skitter. Plaice and cod breed. Crabs scuttle and hide. Rare seabirds – arctic terns and skuas – skim the foaming tops of the breakers.
It adds up to a wildlife wonderland that you can inspect in detail. Enthusiastic parties can join research vessels from the Sven Loven Centre, a marine science unit attached to the University of Gothenburg, which runs educational tours of the area in summer. Minute residents of the Koster fjord are plucked from the seabed and brought into the daylight for closer analysis – and appraisal by expert biologists – in on-board tanks.
Alternatively, there are more weighty creatures – not least the harbour seals that bark and call on rocks west of the islands. On a blustery morning, I see perhaps 30 of them: fat and assured on their lonely outcrop, their relaxed posture a pointed statement to those who come to gawp at them. The nearby presence of the Ursholmen Lighthouse, the most westerly such beacon in Sweden, issues a stark warning that man has not always been so comfortable among these scattered shards.
Life on the Kosters is not confined to worshipful observation, however. Though the islands are host to a permanent population of fewer than 400 souls, there's plenty of activity. Two hours before my meeting with Doris, I had helped to snare the crayfish she so coveted. Nilsson offers fishing jaunts into the fjord, where tourists can assist in reeling in the catch and gain an insight into the islands' working practices.
Nilsson wears a curious expression throughout our trip – perhaps bemusement that anyone would pay to experience the routines of his job. On the other hand, it could simply be contentment. Dragging in the crayfish pots feels weirdly cathartic. There's something satisfying about seeing the pots break the surface, their targets wriggling inside. From there, it's into a bucket, along with any big crabs. Anything unprofitably puny is handed a reprieve over the side.
The gentle approach is ditched once we are back on the dock in Doris's fascinated company. With a total absence of solemnity or squeamishness, Nilsson removes the captives from the boat and dunks them into a vat of boiling water – from which they emerge, piping and delicious. Half an hour later, the full batch is served with great hunks of white bread and dollops of mayonnaise at the nearby restaurant Strandkanten. Outside the window, the light fades above the 50-metre gap that splits the two islands.
This proves to be a scene representative of the general pace of existence here. Indeed, in the nicest possible way, there is little to do on either isle. There are no swimming pools, no amusement arcades, few shops. And crucially, no cars. This is a place to explore in relaxed fashion, on foot, or by bike – the only available form of transport.
On my second evening, I pedal the south island, taking in a landscape that is pastoral Scandinavia at its finest. Narrow lanes cut past clusters of bushes awash with sloe berries, with grassy meadows full of grazing sheep skulk on either side. Red-painted houses hang back in leafy clearings. At Valfjall, a wooden church thrusts its white spire into the pale sky – and at Kilesand beach, on the east coast, a sliver of sand forms a perfect crescent. The only sound is the whirr of my spokes.
It's a similar tale the next day on the north island – after a crossing on the chain-hauled ferry, yellow and clunky, that spans the divide. A pine forest, whispering and fragrant, gives way to the sparse upper tip. In the distance, Norway hogs the horizon.
It is this aromatic calm that has made the islands so popular. Last summer, 300,000 tourists – primarily domestic and Norwegian – pitched up. This counts as a second boom for the region. The first was the herring rush that began in the 1870s and lasted 50 years.
The herring boom's most obvious legacy is the islands' best hotel. Built in 1905 to accommodate the merchants flocking to the Kosters, the Sydkoster Hotell Ekenas found itself without customers when the fish departed almost as quickly as they had arrived. But it survived, and today throws out an arty vibe on the north-east corner of the south island. Photography exhibitions are held in the bar, there's a library on the upper floor and smoked mackerel is doled out for breakfast. The rooms peer at the mainland and the ferries that chug across from the port of Stromstad. At midday, the view is a reminder that these unworldly twins sit remarkably near to the bulk of continental Europe. But as night falls, and silence with it, this odd couple could be thousands of miles away.
*Simply Sweden (0845-8900 300; simplysweden.co.uk) offers a three-night package including return flights from London Heathrow, one night's bed-and-breakfast accommodation in Gothenburg, a 24-hour Gothenburg pass, train and ferry travel to the Koster islands and two nights' bed-and-breakfast accommodation at Sydkoster Hotell Ekenas from £560 per person.
*SAS (0871-521 2772; flysas.com ) flies to Gothenburg from Heathrow; Ryanair (0871-246 0000; ryanair.com ) flies from Stansted; City Airline (0870-220 6835; cityairline.com ) flies from Birmingham and Manchester.
*Sydkoster Hotell Ekenas (00 46 526 202 50; www.sydkoster.se ) has doubles from 1,200SKr (£110) per night, including breakfast.