It is not a task they are facing with relish. Having regained independence from Moscow just five years ago, all three countries believe that the only way they can keep it is by becoming part of the western military alliance.
As the Estonian Prime Minister, Tiit Vahi, put it: "What we really want is a security guarantee in the form of Nato membership as soon as possible. But if it is going to stop short of that then, please, tell us what you have in mind."
Mr Vahi yesterday had the chance to put his point across personally to Nato Secretary General Javier Solana during his brief stop-over in Tallinn.
The content of their private discussion was not revealed. In public, however, Mr Solana restated that none of the 11 countries currently seeking to join Nato had been excluded and that, while not being ruled in, the Baltic states had definitely not been ruled out.
Despite such reassurances in public, Nato officials admit privately that there are more difficulties surrounding the membership bids from the Baltic states than those from other former communist countries, such as Hungary and Poland, which will almost certainly be admitted to the alliance first.
The main problem concerns Russia and its violent objection to any suggestion that the Baltic states could one day join Nato. Russia is opposed to Nato expansion in principle, but is particularly sensitive about the idea of the alliance advancing up to its borders.
On top of Moscow's objections, Estonia and Latvia have the additional complication of containing very large ethnic Russian minorities, while Estonia even has an unresolved border dispute with Moscow.
While celebrating Baltic independence, many Western leaders baulk at the idea of actually being called upon to defend it. As Douglas Hurd, the former British foreign secretary, put it recently: "Is it really credible that the United States or, indeed, Britain would undertake to defend Estonia if this could only be done with nuclear weapons?"
Instead of Nato membership, Mr Hurd suggested that Baltic security concerns could best be met within a defence pact with neighbouring Scandinavian countries, headed by Sweden and Finland, neither of which are Nato members. Under such an arrangement, Lithuania, Latvia and Estonia would clearly come under some sort of Western umbrella, but would not belong to an organisation viewed by many in Moscow as hostile.
On a practical level, Scandinavian countries have already contributed more than others to the building up and retraining of Baltic armed forces, and are happy to go on doing so. They are horrified, however, at the suggestion that they should bear ultimate responsibility for their security.
"This idea is simply unworkable," said a Scandinavian diplomat in Tallinn. "The Nordic countries are happy to complement Nato assistance here, but they cannot replace it."
Baltic leaders themselves fear that given recent moves in Russia towards recreating something of a union with former Soviet republics, exclusion from Nato will allow Moscow to think that they have fallen into a "grey zone".
"For us a `grey zone' would be a very black scenario," said Mari-Ann Kelam, Estonian foreign ministry press spokesman. "It could leave the impression that we were up for grabs."
To counter this impression, Baltic politicians would seek to step up their involvement in Nato's Partnership for Peace programme and would like to invite many more forces from Nato countries to participate in joint training exercises on Baltic territories.They are also planning to step up their efforts to join the European Union.