Robredo, of Spain, was the tournament runner-up in 2005.
Calleri, of Argentina, was a semifinalist last week in Barcelona, Spain, and played in the Estoril final in 2003.
Third-seeded Serbian Novak Djokovic beat Guillermo Garcia-Lopez of Spain, 6-4, 1-6, 7-5; fifth seed Richard Gasquet of France downed American Vincent Spadea, 6-3, 6-4; and France's Paul-Henri Mathieu beat Juan Monaco of Argentina, 6-4, 4-6, 6-1.
"You've got to look on the positive side, it's always good to win a really difficult match," said Djokovic. "Today's match had a lot of unforced errors."
Robredo meets Djokovic in Saturday's semifinals, while Gasquet plays Mathieu.
LGBT community has 'bullied the American people': Bachmann
Duggar sisters unveil Christian dating rules in new book