I have always believed that the best holidays are the ones where you accidentally take a wrong turn and end up somewhere brilliant. Our recent trip to Desenzano del Garda proved this theory beyond any doubt, though the journey there very nearly ended my marriage.

We had picked up our hire car at Milan Bergamo, full of that particular swagger you get from having successfully navigated an airport in a foreign language. My husband was driving, I was in charge of navigation, and within forty minutes we were hopelessly lost somewhere near Brescia. The sat nav had decided to have a small nervous breakdown, my phone had no signal, and I was insisting we should "just follow the lake" as if Lake Garda were visible from every hillside in Lombardy. Three increasingly tense circuits of a roundabout later, we found ourselves on a single-track road between vineyards, me stubbornly pretending this had been the plan all along, him gripping the steering wheel with the quiet fury of a man who knows better but has learned not to argue.

Then something wonderful happened. The road dipped down through an arch of cypress trees and suddenly there was Desenzano spread below us, the lake impossibly blue, the whole scene so ridiculously picturesque that we both burst out laughing. The argument evaporated. We had arrived by accident, and it felt exactly right.

Our apartment was down in the old town, a proper local place with shutters that clattered in the morning breeze and a balcony just big enough for two chairs and a bottle of wine. But I am getting ahead of myself. That first evening, determined to stretch our legs after the drive, we wandered out with no particular destination and promptly got lost again within five minutes. The old town is a maze of narrow lanes that seem designed to confuse people exactly like us. We turned left, then right, then found ourselves in a tiny piazza with a fountain and no idea how to get back.

This is how we discovered the bakery. It had no sign to speak of, just a green door propped open and the smell of something extraordinary drifting out. Inside, an elderly woman was pulling trays of sbrisolona from the oven, that crumbly almond cake particular to this part of Italy. We bought a slice wrapped in paper, ate it standing in the street, and it remains one of the best things I have ever tasted. We tried to find it again the next day and failed completely. I am not convinced it actually exists in any conventional sense.

The following morning we set out to find the harbour, which according to our map was straightforward. It was not straightforward. We ended up on the wrong side of the railway line somehow, walking through a residential area where washing hung between balconies and old men sat on plastic chairs watching us with the amused tolerance of people who have seen many lost tourists. A woman gestured us down an alley we would never have noticed, and we emerged onto a pebble beach so small and perfect that we spent the entire morning there, swimming in water so clear you could see every stone on the bottom. No umbrellas for hire, no cafe, just us and a few local teenagers who seemed mildly surprised to see us.

That became our pattern. Deliberately vague plans, followed by cheerful incompetence, followed by accidental discovery. We found a wine bar down a passage so narrow I had to turn sideways, where the owner poured tastings of Lugana and told us about his grandfather's vineyard in completely unintelligible Italian that we nodded along to with fraudulent understanding. We stumbled upon a Tuesday morning market that filled a car park near the castle, selling everything from socks to fresh sardines, and ate the most enormous arancini at a stall run by a man who called me "bella" with such rote professionalism that it actually made me laugh out loud.

The castle itself we found by following a cat. I am not proud of this, but there it is. A tortoiseshell was strolling up a steep lane and we followed it, as you do, and arrived at the top with spectacular views across the lake and absolutely no memory of how we had got there. We sat on the wall and watched the ferry boats crossing to Sirmione, feeling terribly pleased with ourselves for having discovered this spot, though of course the castle is well known to everyone except people who follow cats for directions.

By our final day we had given up even pretending to know where we were going. We walked until something looked interesting, then investigated. This is how we found the little harbour at Rivoltella, south of the main town, where local families were swimming and an old man was fishing with a hand line, catching nothing whatsoever with the serene patience of someone who has never expected to. We stayed for hours, swimming out to a floating platform and lying in the sun like seals, then found a pizzeria nearby that had no English menu and made us a pizza with porcini mushrooms that I still think about when I cannot sleep.

I suppose there is a lesson in all this, though I am wary of people who find lessons in their holidays. Perhaps it is simply that getting lost is underrated, that the places you find by accident often stay with you longer than the ones in guidebooks, and that my sense of direction is genuinely terrible but occasionally useful. We left Desenzano with no photographs of famous landmarks, no checked-off lists, just a collection of small moments that belonged to us because we had wandered into them uninvited. The sat nav never really recovered, incidentally. We named it Giuseppe and learned to ignore it with affection.