Czech election: two candidates in second round run-off
With almost all the votes counted in the first round of voting, Mr Zeman has emerged as the front runner, with Mr Schwarzenberg in second place.
The two candidates will now contest a run-off in two-weeks time, as no candidate won 50% of the votes.
Another former Prime Minister, Jan Fisher, was beaten into third place.
He had previously led the polls but failed to shine in a pre-election televised debate among candidates.
Vladimir Franz, a drama professor, painter and composer who is covered in blue tattoos, came fifth.
The BBC’s Rob Cameron, in Prague, says the result means the election to succeed President Vaclav Klaus, who led the country for ten years, now centres around two very different men.
Milos Zeman is a hard-drinking, chain-smoking politician, known for his witty put-downs of his political opponents, our correspondent says.
Karel Schwarzenberg is a titled prince, 75 years of age but wildly popularly amongst young, urban voters – and closely linked to the country’s first president, the late Vaclav Havel, he adds.
Playwright and dissident Vaclav Havel was the leader of the Velvet Revolution that brought down Communist rule in 1989.
Mr Klaus, a charismatic but divisive figure, is barred by the constitution from seeking a third term in office.
Correspondents say his departure is likely to be welcomed in many European capitals, which were often exasperated by his blunt suspicion of European integration.
However, many in the Czech Republic gave him credit for his economic policies when in government in the 1990s, and for his decision to keep out of the euro.
The vote is the first time the president is being directly elected by the pubic.
The new president will represent the Czech Republic abroad and appoint candidates to the constitutional court and the central bank, but does not carry much day-to-day power.