Among those paying their respects were Vice President Joe Biden, three Pennsylvania governors and federal judges.
The state's longest serving senator is being remembered as a political moderate who wasn't afraid to buck the leadership of his own party.
"I've never seen as much undaunted courage as Arlen had - both physically and politically. He believed he could change the world, if he just worked hard enough at it," Biden told mourners.
Specter, who was 82, died at home of complications from non-Hodgkin lymphoma on Sunday.
He was first a Democrat, then Republican and then just three years ago, switched back to the Democratic Party. He had spent 30 years in the Senate before losing his seat in 2010 after crossing party lines to vote for President Barack Obama's stimulus package.
"In a dark time for our nation, he was willing to lose his seat to cast a decisive vote," said Specter's son Shanin, whose remarks capped about 90 minutes of tributes.
Anthony J. Scirica, the chief judge on the 3rd U.S. Circuit Court of Appeals, called Specter "irreplaceable."
"He touched so many lives," Scirica said. "He had some tough times, but he always thought that he was working for the public good."
The Associated Press contributed to this report.