Mart Laar shows the prince his "paperless" system
But despite sub-zero temperatures Prince Charles received a warm welcome at a reception hosted by the British ambassador at Kadriorg Palace, in the capital Tallinn.
Greeted by Estonia's Prime Minister, Mart Laar, and President Arnold Ruutel, the prince also met Derby County Football Club's towering goalkeeper, Mart Poom, and Estonia's Olympic decathlon gold medallist, Erki Nool, at the reception.
Earlier Mr Laar took the opportunity to demonstrate the "paperless" system used by the Estonian Cabinet.
The premier explained that cabinet business was conducted on computer terminals - making environmentally unfriendly reams of official documents unnecessary.
Later at an official dinner the prince gave President Ruutel a carriage clock and signed photograph of himself.
And the president gave him two lithograph prints of flowers.
The prince then told guests that the world had been "filled with admiration" by the way Estonian people had helped lead the revolt against the Soviet Union.
In Lithuania the prince will visit the remains of barricades created when two million people formed a human chain in defiance of Soviet rule.
And in Latvia Prince Charles will lay a wreath at a monument to freedom and meet Holocaust survivors.
Democratic civilisation
The prince said his trip was "symbolic" of Britain's support for the former Soviet republics.
The three countries have been independent since the Soviet Union collapsed 10 years ago, partly because of their defiance.
Writing in the Daily Telegraph, Prince Charles said the Baltic states were "a beacon of stability and freedom".
"At a time when the values of Western democratic civilisation are under threat, it is timely to remind ourselves of the sacrifices made by others to attain the freedom that we in Britain have always taken for granted."
'Overwhelming support'
Prince Charles said the Baltic states matter to Britain, as does their commitment to joining the EU and Nato.
"My visit will help to symbolise Britain's overwhelming support of their efforts to do this," he said.
An orphanage in Daugavpils, eastern Latvia, is also on the royal agenda, as are organic farms in all three countries.
The prince said he would also attend a British-supported army training exercise in Lithuania and see other British initiatives to help modernise the armed forces in the Baltics.
"As our armed forces find themselves engaged in operations on another side of the world, it's good to know that we have friends in Europe about whom we may think we know a little, but who look up to this country as a beacon of stability and freedom."