At first glance, the northernmost speck on the map of Orkney could easily be overlooked. Yet, the rocky shore of low-lying North Ronaldsay is anything but ordinary. Venture to this tiny Scottish isle and you'll find the tallest land-based lighthouse in the UK, the ruins of an Iron Age broch (a type of drystone roundhouse) and – most bizarrely – a flock of wild-eyed short-legged sheep with a diet that's as unusual as their remote habitat.

North Ronaldsay sheep are one of the oldest and rarest breeds in the world. They are descended from traditional Orkney sheep, a species of Northern European short-tail sheep, that were seen across the Orkney Islands for centuries. However, in most places, the small, slow-growing sheep eventually made way for breeds better suited to large-scale, commercial farming such as Cheviots and Leicesters.

But not on North Ronaldsay. Here, the local farmers' deep attachment to the animals and unconventional approach to tending them ensured the island's traditional sheep were retained – and they remain intertwined with the island's identity today.

Taking the morning ferry from Kirkwall, Orkney's main town, I sailed the 36 miles north, binoculars glued to my eyes watching black guillemots bobbing in the water and the odd gannet and fulmar swooping across the stern. Getting to North Ronaldsay is very much in the hands of the weather and tidal gods. Orkney Ferries operates a two-and-a-half-hour service from Kirkwall, which can be somewhat unpredictable; while Loganair runs multiple 17-minute flights daily that are also weather dependent.

I disembarked under a welcome blue sky to find a bicycle leaning against the small ferry terminal, as promised by North Ronaldsay bike hire. At around four miles long and two miles wide, and with virtually no public transport, North Ronaldsay's gently rolling landscape is best navigated on two wheels and this was the logical way for me to go sheep-spotting.

A few wheel-turns up from the pier was the North Ronaldsay Bird Observatory, the beating heart of the community. The island is a popular stopping-off point for migratory birds, such as whinchats, wheatears, spotted flycatchers and, if you're lucky, rare bluethroats, and this centre monitors them all. It also has a restaurant where some of the island's 50 inhabitants come to dine (I spied "North Ronaldsay mutton" scrawled on the chalkboard) and overnight accommodations for visitors.

It's also where Heather Woodbridge, an instantly impressive young woman who wears many hats – including those of deputy leader of Orkney Islands Council, director of The North Ronaldsay Trust and trustee of The Orkney Sheep Foundation – helps out as an administrator. In addition, she manages a flock of North Ronaldsay sheep, which I could see grazing between the picture windows and the sun-dappled bay.