Before leaving for Florence, the British Prime Minister admitted to anxiety over his wife's unexpected pregnancy at the age of 45. "We are quite old to have a baby," Mr Blair said. "I admit, I am just a wee bit apprehensive."
Last night they were attending a dinner at which Cherie's good friend Hillary Clinton was receiving a prize from New York University. Mrs Clinton was one of the first to phone Downing Street to congratulate Mrs Blair; now she could repeat the good wishes in person.
It was all a lot more congenial for the President and his wife than Athens, their previous stop, where anti-American protesters had trashed shops and set fire to banks and cars to show their outrage at the man who waged war in the Balkans.
The event the Blairs and the Clintons were attending in Florence was a quiet gathering of like-minded leaders - though last night the motorcades of five European premiers, as well as those of the US and Brazilian Presidents, clogged the streets of the Renaissance city for what rapidly, if inexplicably, developed into a mini-summit.
Billed as another Third Way event, the conference went officially under the more neutral title: "Progressive Governance in the XXI century", in deference to more traditional socialist participants, such as France's Lionel Jospin. It is a follow-up to a seminar in New York last autumn at which Mr Clinton, Mr Blair and Romano Prodi, then the Italian prime minister, debated their centrist political agenda with leading academics.
But a year is an eternity in politics, and today's host, Mr Prodi, now finds himself in a different job, as president of the European Commission. In the meantime, Mr Blair's status as the star turn of Europe's centre- left has faded, challenged by the economic success of Mr Jospin's government and by New Labour's drubbing in the June Euro-elections.
As with all the best parties, the organisers had difficulties with the guest list. Although Mr Prodi is no admirer of his more left-wing successor, Massimo D'Alema, the new Italian Prime Minister could not be left out of such a meeting - in Italy. Naturally, the Italian President, Carlo Azeglio Ciampi, is also taking part, as are the Foreign Minister, Lamberto Dini, and the Treasury Minister, Giuliano Amato.
A host of academics is on hand, as well as some of those unable to attend in New York, including the Brazilian President, Enrique Cardoso. Gerhard Schroder, the German Chancellor, is in town, too - all of which has made it irresistible for Javier Solana, Europe's new foreign policy supremo.
Most eyes will, however, be on the body language between Mr Blair and Mr Jospin, whose attendance underlines a truce in an ideological tussle on Europe's left.
That debate began last summer, despite early signs of consensus when the French premier coined a soundbite in London - "Yes to the market economy, no to the market society." But last autumn in New York, Mr Blair sought to flesh out his Third Way, a vague mix of centrist politics, globalised economics and social justice.
Earlier this year Mr Jospin was piqued when Mr Blair agreed a joint paper with Mr Schroder. Mr Jospin, however, had the last laugh when in the Euro-elections the British and German left were trounced, while the French left prospered.
But when the leaders get down to business today in the Salone dei Cinquecento in the Palazzo Vecchi, the outstanding ideological tensions are likely to be avoided
And how to control the proliferation of summits - let alone the proliferation of leaders' offspring - is not on the agenda.