But the day had many touches of humor as friends recalled his remarkable career - and his obsession with squash.
While Rendell said "I meant it" when he told a friend that the 30-year veteran of the Senate did more for the state than Franklin, he was quick to add that if they actually had met, the colonial jack of all trades would have bragged of his scientific discoveries while Specter would have told him "how to mix a perfect martini."
While Specter's long career was marked by his political centrism and two changes of party, his friends said personal loyalty was a defining trait. They said he stuck by his friends and allies even when it hurt him politically.
Biden, who passed up campaigning in two battleground states during a close presidential election to attend the funeral, was happy to return the fealty.
"I ask myself, 'What would Arlen do?' Arlen wouldn't have even thought about it. Arlen would have been there for me," Biden said.
He also recalled that Specter had offered to make a TV ad for Biden, a Democrat, during a tough 1990 reelection campaign even though Specter, then a Republican, was going through a difficult time himself with the Supreme Court confirmation hearings for Clarence Thomas.
"I said, that makes no sense. You already have problems," Biden recalled. But Specter made the 30-second spot and sent it to his friend anyway.
"Does anybody know anyone in politics who would have done that?" he said.
He joked that Specter persuaded him to appoint so many Pennsylvania judges when they were on the Senate Judiciary Committee that Specter used to tell him, "Remember, you're Pennsylvania's third senator."
Summing up his friend, with whom he often rode to Washington on Amtrak, he said: "I've never seen a man with such undaunted courage as Arlen. He was both physically and politically courageous. He believed you could change the world."
Rendell also remembered Specter for his devotion to fairness. When Rendell was district attorney and Frank L. Rizzo was mayor, he recalled, he could get money from the mayor by telling him, "It's a war out there." When Rendell was mayor and governor, he would make his case to Specter by saying, "It's the fair thing to do. . . . It always worked."
Even when Specter was cross-examining Anita Hill during the Thomas hearing, Rendell said, he knew it would get him in trouble with women who thought he was too harsh, "but he believed it was the right thing to do."
Rendell said he last saw Specter after his illness returned and he was in the hospital. Specter was weak and in a wheelchair, but in his usual commanding manner, he told Rendell to tell the nurses to let him walk because he needed exercise.
"I was exhilarated. He was as feisty as ever. I thought, he's going to make it," Rendell said.
As late as October, Specter told his wife, Joan, the former city councilwoman and pie-making entrepreneur, that he wanted to teach one more class on the Supreme Court confirmation process at his alma mater, the University of Pennsylvania. He did, on Oct. 4.
If Biden's speech was all emotion and Rendell's was peppered with jokes, Specter's son, Shanin, gave a passionate eulogy to his father that could be condensed into five words: He was a great man.
He was proud of and encouraged his family, from his wife's political and culinary efforts to his sons and granddaughters.
"His watchwords were always praise and encouragement," said Shanin Specter, a lawyer in Philadelphia. His brother, Steven, is a microbiology and immunology professor in Florida.
He was the "patron saint of lost causes," fiercely independent, and not the least interested in money. When a secretary stole his life savings, he ended up forgiving her, his son said.
What Specter couldn't do without was his daily game of squash, a sport whose love he passed on to his sons and granddaughters.
Shanin Specter said his father told him that squash was "the most important thing that I do every day. He later amended that to the only important thing I do every day."
Most of the honors and accomplishments the public already knew. But there was a side of the man that he reserved for a few special people; just four, in fact. His grandchildren.
Silvi Specter, a student at Penn, said her grandfather "worked tirelessly to be the best grandfather he could be and he always succeeded."
He was her role model, she said, and inspired and approved of her career goals: lawyer, then senator, then president of the United States.
The audience applauded.
Contact Kathy Boccella at 610-313-8123 or firstname.lastname@example.org, or follow on Twitter @kmboccella.