"Scott's curiosity knew no bounds," said Glenn, who preceded Carpenter into space 51 years ago as a member of the Mercury 7 program, America's first corps of astronauts.
Glenn was the first American to orbit Earth and Carpenter was the second, both traveling in one-person capsules. Glenn, now the last surviving Mercury astronaut, delivered Carpenter's eulogy.
Carpenter, who lived in Vail, Colo., died Oct. 10 of complications from a stroke he suffered in September. He was 88.
When Carpenter orbited the Earth in 1962, he had to take manual control of his spaceship because of instrument problems and low fuel, and he splashed down hundreds of miles off-target.
That troubled flight created a rift between Carpenter and NASA bosses, and he never flew in space again. But he turned to sea exploration, and in 1965, he spent 30 days under the ocean off the California coast in the Navy's SeaLab II program.
On Saturday, nine other astronauts, Colorado politicians and dozens of friends and family members joined Glenn at Carpenter's funeral at St. John's Episcopal Church in Boulder.
Glenn and Carpenter became friends during astronaut training, and it was Carpenter who gave Glenn his memorable blessing as Glenn prepared to launch into space: "Godspeed, John Glenn."
"Godspeed, Scott," Glenn said Saturday, and then paused as emotion overtook his voice. "You are missed."
Carpenter was born May 1, 1925, in Boulder and graduated from high school there before serving in the Navy in World War II and the Korean War. He was chosen for the Mercury space program in 1959.
Glenn recalled NASA subjecting the astronauts to a barrage of punishing tests and probing psychiatric questions. Most of the astronauts considered it something they had to endure to fly in space.
"Scott seemed to really enjoy these tests," Glenn said, drawing laughter.
Carpenter loved music, Glenn said, and requested the hymn "Be Still My Soul" be sung at his funeral. Glenn also recalled a time he and Carpenter tried to harmonize on the song "Yellow Bird."
"We weren't much good," Glenn recalled Carpenter saying, "but we were loud."
NASA Administrator Charles Bolden, who also spoke at the funeral, called Carpenter a tireless explorer and an unforgettable character. Bolden said he was just a teen when Carpenter orbited the Earth and remembered "being tremendously moved by his bravery."
"Today, we bear witness as he soars once more into the heavens on his journey to eternity," Bolden said.
Carpenter's flag-draped casket was carried into the church by six Navy officers as a bell tolled from the church tower. After the service, four F-18 fighter jets flew the missing-man formation over the church against a cloudless autumn sky.
Carpenter is survived by his wife, Patty Carpenter, and six children. Two other children died before him.
His ashes will be interred at his ranch near Steamboat Springs, Colo.