Today you can freely inspect the crumbling rocket sites and radar installations once so jealously guarded by the Russians, which are gradually being reclaimed by the pine forests and juniper groves typical of the entire island.
But most visitors go for the peace of its small towns, sandy beaches, cliffs, empty roads, windmills and picturesque wooden houses.
Some things are changing to accommodate tourists - who come mostly from Finland, attracted by the island's low costs and liberal attitude towards alcohol. There is an incongruous Irish theme pub and a John Bull Inn given over to rock'n'roll and tsiklisopradele (motorbike fans). Yet with over 1,000 square miles and a population of 40,000, it is easy to enjoy the calm of an unspoilt countryside brimming with wild flowers and birds.
The capital city, Kuressaare, still has the atmosphere of a frontier town. But it has an efficient tourist service, which finds accommodation in local farmhouses and quite pleasant hotels. Bikes, boats, tents, cars and horses can all be hired.
Every June there are highly professional classical music and folk concerts in the grounds of the imposing 14th- century castle overlooking the town. There are adequate places to eat, all serving what is held to be the best beer in Estonia. Food can sometimes be heavy - fearsome dumplings and pallid sausages - but salads are delicious, as are the caviare and smoked fish.
Estonia remained pagan until the 13th century, and the renegade local who first let in the Christian knights is still viewed as a national disgrace. A surviving heathen culture is still evident in the local churches: the odd pentangles on the ceilings and jolly murals of bare-breasted young women.
Life is as regular and soothing as the windmills in front of which newly- weds traditionally lay stones inscribed with their names.
Those in need of more excitement can always visit the eighth-century meteorite crater at Kaali - the first proven site in Europe. Who cares that today it looks like little more than a sunken village pond? Saaremaa is a place for rest, not sudden shocks.
Other evidence of history includes German fortresses, Orthodox churches, a spa park and an open-air museum with 100 traditional houses. This is on the neighbouring island of Muhu, joined to Saaremaa by a narrow causeway. Out on the Sorve peninsula, there is a reminder of more recent history; a sword monument commemorating a fierce hand-to-hand battle in October 1944 between retreating German troops and an Estonian rifle division.
Estonians who sided with the Germans, or were thought to be unenthusiastic about the Soviet re-occupation, left the island or disappeared, leaving the population even more depleted. But there are still enough people to mind the amber stores and sell hand-knitted sweaters at a fraction of the price they would fetch in the West.
Access to Saaremaa is by ferry from Virtsu just outside Estonia's capital Tallinn - itself still one of the most beautiful and unspoilt of European towns. Taken together, a visit to this lovely medieval city and to the island should make for an interesting, unusual and utterly serene holiday.
Baltic Fact File
Reaching Latvia and Estonia (as well as the third former Soviet Baltic republic of Lithuania) is much easier than it used to be in the days of the USSR. British Airways (0345 222111) flies daily from Gatwick to Riga, with a World Offer fare of pounds 199 return. Tallinn is served daily except Saturdays from Gatwick by Estonian Air (0171-333 0196) for pounds 250. Lithuanian Airlines (0181-759 7323) and BA serve Vilnius from Heathrow and Gatwick respectively.
Cheaper flights may be available on indirect routings such as SAS via Copenhagen or Stockholm, or Austrian Airlines via Vienna.
Interestingly, if you book a city-break package you can sometimes actually undercut the air fare. For example, the specialist operator Regent Holidays (0117-921 1711) has a three-night stay in Tallinn from January to March for just pounds 199, including the hotel.
British passport holders travelling as tourists no longer require visas for any of the three republics.