Puigdemont's visit to Denmark could help him avoid problems in Belgium, where European citizens can live without a residency permit for three months, after which they theoretically have to leave.
Puigdemont's journey, which included attending a university debate and meeting Danish lawmakers, came almost three months after he was removed from office and fled to Belgium.
His proposed appearance at the debate in the Danish capital comes while Puigdemont is trying to be reinstated as the regional president of Catalonia.
Puigdemont was charged after he fled Spain.
Junts Per Catalunya and ERC both support Puigdemont. The fugitive former leader of Catalonia has arrived in Denmark, despite threats from Spain to seek his immediate arrest there. The Faeroes are holding a referendum on a new constitution on April 25.
Spain's foreign minister says that "for the moment" ousted Catalan leader Carles Puigdemont is free to move in Europe outside of Spain, adding that his arrest was a matter for judges to decide.
The parliament was dissolved a year ago by the government in Madrid after the body approved the region's unilateral independence.
He called for a meeting with Spain's prime minister Mariano Rajoy in a bid to reach a resolution to the situation.
In Copenhagen, Puigdemont declined to comment any further on the day's events. That decision was made amid fears that the Belgian judge would strike out the most serious charge of rebellion, with consequences for the prosecutions of those in jail or on bail back in Spain.
Earlier, the Catalan parliament's speaker, Roger Torrent, said Mr Puigdemont's candidacy to head the regional government was "absolutely legitimate" despite the charges against him. Whether or not Puigdemont can lead Catalonia in absentia has been debated hotly.