"He was good company, my friend, Ted," the Arizona Republican said. "He had the Irish talent for storytelling and for friendship."
In particular, McCain recalled an argument between the two on the Senate after they noticed two freshman senators arguing.
"You might think that two more senior members of the Senate would in such a situation counsel two junior members to observe the courtesies and comity, which, theoretically, are supposed to distinguish our debates," he said. "But Ted and I shared the sentiment that a fight not joined, was a fight not enjoyed. And irresistibly we were both drawn into a debate we had no particular interest in, but which suddenly looked like fun."
"I struck first, castigating the young Democratic Senator for abusing my Republican colleague. Before she could respond for herself, Ted rode valiantly to her rescue. And within minutes, he and I had forgotten why we were there, and what the debate was all about. We had probably even forgotten the names of our two colleagues. As one of us spoke, the other would circle the floor, agitated and anxious to fire back.
After a while, we must have thought the distance between our desks too great for either of us to hear each other clearly or that the presence of the clerk transcribing our exchange had become too distracting. And as if we had both heard some secret signal, we set down our microphones simultaneously and walked briskly to the well of the floor, where we could continue in closer quarters, and in language perhaps too…familiar…to be recorded for posterity, which, regrettably was still audible enough to be overheard by a few reporters, who were now leaning over the railing of the press gallery trying to ascertain just what the hell was going on between McCain and Kennedy."
CBSNews.com Special Report: Ted Kennedy
CBS News Special Report: Ted Kennedy - The Last Brother
McCain also talked about working with Kennedy on immigration reform legislation a few years ago, saying he was the "most reliable, the most prepared, and the most persistent member of the Senate."
"We had a daily morning meeting with other interested senators. He and I would meet for a few minutes in advance, and decide between us which members of our respective caucuses needed a little special encouragement or on occasion a little straight talk. If a member tried to back out of a previous commitment, Ted made certain they understood the consequences of their action. It didn't matter to him that the offender was a member of his own caucus," McCain said. "And though on most issues I very much wished he would give up, he taught me to be a better senator."
McCain concluded his remarks with the following sentiment: "After Labor Day, I'll go back to the Senate, and I'll try to be as persistent as Ted was, and as passionate for the work. I know I'm privileged serve there. But I think most of my colleagues would agree, the place won't be the same without him."
Read more on tonight's memorial service on CBSNews.com:
Family, Political Luminaries Honor Kennedy
Caroline Kennedy: We Have to Do What He Would Have Done
Biden: Kennedy's Legacy Is How We Look at One Another
McCain: Senate "Won't Be the Same" Without Kennedy
Kerry: Kennedy's Gift Was "Incomparable Love of Life"
Hatch: Kennedy and I Were Like "Fighting Brothers"
Dodd: "Teddy Changed Our America"
Rep. Joseph Kennedy: Teddy Was Always There
Photos: The Scene at the JFK Library Memorial
Photos: Speakers Pay Tribute to Kennedy