Footballing god Cristiano Ronaldo even lends his name to the airport, which has a statue of the Portuguese superstar outside.
It’s a replacement after the first attempt — unveiled at the airport’s opening — was mocked worldwide.
Among my family’s to-do list on our trip is a visit to the Cristiano Ronaldo museum.
But don’t be fooled into thinking that this Portuguese island in the Atlantic Ocean is the footballer’s own branded resort — there is so much more to Madeira.
It is dubbed the island of eternal spring because it provides all-year-round sun.
It also means there is an array of spectacular flora and fauna on show.
After a very short transfer, we arrive at the all-inclusive 4H Riu Madeira hotel, where we check into two interconnecting rooms, perfect for my wife and I and our boys, aged 14 and 12.
Our Tui rep Miloslawa greets us and gives us some important tips: Never listen to the weather forecast as the conditions can change in minutes.
Always wear clothes suitable for rain and sun.
And try the local drink called poncha.
We were also urged to visit the local carnival parade in nearby Canico, which we instantly took her up on.
February is party time for the islanders and there are Rio-style jamborees all over.
Floats carrying glamorous dancers and circus acts brought the town to a standstill, with everyone in fancy dress — and some opting for Ronaldo kits, of course.
The following day we took an excursion to the east coast in an off-road 4×4 Range Rover with Sustainable Tours.
It took us to Pico do Arieiro, one of the highest peaks, where we went from balmy temperatures to seeing our freezing breath within a half-hour’s drive.
Many come to hike the eight-mile mountain trail to the even higher Pico Ruivo but there is no time for us as we need to zip back down through the incredible woodland.
Madeira is actually translated from the Portuguese for wood and refers to the trees explorers found when they first set foot on the island
The unique laurel trees, which still exist here, mean they have Unesco status as an outstanding area of natural beauty
The scenery was breathtaking, but so was being thrown about on the back of the Land Rover with its roof rolled down.
My sons Luke and Jake said it was like Alton Towers.
We then went to meet local farmers, who gave us a lesson in chopping down sugar cane — once one of the island’s main industries.
One use of the cane is for making the poncha drink. It is a blend of sugar and rum from a recipe handed down from the first explorers there.
But too many and any hopes of further exploring the island would quickly come to an end.
We whipped up a jug and sipped at the sugary spirit while taking in our spectacular surroundings.
Poncha may be the natives’ favourite tipple, but wine is their most famous.
Since the 15th century, they have sold their distinctive fortified plonk by the barrel-load round the world.
We were taken to Blandy’s showroom to be given a tasting test.
Interestingly, the wine doesn’t mature with age, but it is by shaking it in barrels that you achieve its best taste.
Back at the hotel, we definitely needed a lie down at the pool, where you can take advantage of the all-inclusive bar.
The restaurant buffet kept us well fed all week, with tasty dishes including some delicious Portuguese pastries.
We could then relax in the evenings with live music while using the Tui app to find our next place to visit.
The capital Funchal is home to most of the sights and is just a free bus ride away from the hotel.
But there is still lots of hard walking to be done.
It felt like no single 100m stretch of the quaint cobbled streets was on a level.
One of the top attractions is the toboggan run down one of the city’s steepest roads.
Sliding along on a creaking wooden wicker basket — pushed by two burly drivers at speeds reaching 20mph — is great fun.
It’s their equivalent to gondoliers pushing through Venice canals, but it’s down tarmac and whizzing past cars.
Another way to get about is the cable cars, which take you out of the centre into the suburbs and botanical gardens.
In the centre, the impressive cathedral and bustling farmers’ market — with strange fruit, vegetables, flowers and fish — provide a great way to while away a few hours.
And before jetting home, we made it to Cristiano Ronaldo’s museum, which hosts his incredible trophy haul.
Never shy and retiring, the former Man United ace also has lifelike mannequins of himself to pose with.
Or you can pop upstairs to the CR7 hotel for a glass of champers in the Offside bar.
But I think I’ll stick to the poncha.
GETTING THERE: Seven nights’ all-inclusive this summer at the 4H Riu Madeira is from £816pp including flights from Manchester on June 9 and transfers, or from £1,008pp in August, departing August 11.
Based on two adults and two children sharing.
To book, go to tui.co.uk or download the app.