Also doing well is former President Clinton, who had heart surgery in September, a former aide said.
Cheney, who has had four heart attacks, had three hours of tests Saturday after experiencing shortness of breath. They showed no problems with heart "none whatsoever," said Mary Matalin, a former top White House aide to the 63-year-old vice president.
"He's fine," said Matalin, who has acted as his spokeswoman this weekend.
Cheney's most recent heart attack was in November 2000, just before he assumed the vice presidency. He had a pacemaker implanted in his chest in June 2001.
Matalin said Cheney was just following the orders of his "very cautious" doctors who recommended that he have tests at the hospital. Cheney returned Thursday night from a pheasant hunting trip in South Dakota with a cold that left him short of breath.
She said in a broadcast interview that Cheney should serve as "an inspiration to people with heart disease that you can lead such a productive and constructive life." She noted the vice president's heavy travel schedule during the presidential campaign, saying Cheney attended more than 280 events.
"It was a remarkable schedule," she said. "The long and the short is, the vice president had a cold like everybody else did on his plane."
President Bush, at services at St. John's Church across the street from the White House, heard the minister offer prayers for Cheney.
As for the 58-year-old Clinton, he has lost some weight since quadruple bypass surgery Sept. 6 and gets tired at night, said Democratic strategist and former top aide James Carville.
But that is to be expected and he pronounced Clinton "ready to go he's rolling," said Carville, who appeared with Matalin, his wife.
Clinton sat out most of the presidential race and emerged to campaign for Democrat John Kerry just a week before Election Day. The former president looked pale and unusually thin.
Clinton's $165 million presidential library is due to open this week, with a dedication ceremony planned for Thursday. Bush is scheduled to attend.