Cheney said serving under four presidents taught him that a surprising international crisis is inevitable.
"When I think about the kind of individual I want in the Oval Office in that moment of crisis, who has to make those key decisions, some of them life-and-death decisions, some of them decisions as commander-in-chief, who has the responsibility for sending some of our young men and women into harm's way, that man is Mitt Romney," Cheney said to applause.
It was a strong endorsement from a man who has come to represent the neoconservative foreign policy wing of the Republican Party. Until Thursday, Romney had avoided appearing with Cheney or with Bush.
Cheney, who generally avoids retail politicking, is still a controversial figure because of his hawkish foreign policy stances and support for enhanced interrogation techniques - like waterboarding - that many consider torture. Democratic President Barack Obama banned those techniques after he took office.
Donors gathered Thursday night under a tent next to the driving range at Teton Pines Country Club, a golfing community where Cheney has a home. After Cheney introduced him, Romney praised the former vice president as "a great American leader."
Romney criticized Obama's domestic policies on health care and spending. "But the foreign policy mistakes, I believe, may be even longer lasting in their negative impact on the country," he said, but he did not specify those policies. In the past Romney has attacked Obama's policies on Iran, China and Israel, although he has praised the president for authorizing the raid that led to the death of Osama bin Laden.
Romney raised more than $4 million with Cheney, long a strong fundraiser in part because of his popularity among the conservative Republican base. The Cheney-sponsored events in this resort area near Yellowstone National Park represent a welcome endorsement for Romney, who is eager to win over more of the party's base.
Cheney was hosting Romney at a private dinner at his Wyoming home after he posed for photos with Romney and the fundraisers who had flown from all over the country for the event. They were drawn either by Cheney or by the dramatic beauty of the mountains in this resort valley. New York Jets owner Woody Johnson, a national campaign finance co-chair, was in attendance, as were bundlers from Texas, Arizona, Oklahoma and New York, among other places.
Oklahoma City oil magnate Harold Hamm, frequently mentioned in Romney's standard campaign speech as an inspiring rags-to-riches example of American entrepreneurship, also attended. Hamm drove a truck to put himself through college before striking it rich in North Dakota.
"Harold's doing just fine, by the way. How you doing, Harold?" Romney called out, as the crowd laughed. "Forbes publishes his net worth on a regular basis."
Hamm is No. 78 on Forbes' list of the world's billionaires, worth $11 billion, according to the magazine.
Attendance at the dinner with Cheney cost $30,000, though many had already contributed that much before Thursday night's event. Cheney's red-doored home is at the end of a cul-de-sac and overlooks the golf course and the Grand Teton mountain range. The Secret Service had set up metal detectors on the back lawn in preparation for the dinner.
Romney doesn't have a close personal relationship with the former vice president. While he speaks regularly with former President George H.W. Bush, Romney seldom refers by name to the most recent Bush to occupy the White House. On occasion he goes out of his way not to say Bush's name out loud and simply calls him "the predecessor" to Obama.
Romney has embraced Cheney in the past. Last year, he told an Arizona town hall that Cheney's "wisdom and judgment" would provide a model for choosing his own vice president.
Many of Romney's policy advisers were officials in the Bush White House. Former Secretary of State Condoleezza Rice recently endorsed the former Massachusetts governor. On Thursday, Romney aides refused to comment on reports that Rice is a top consideration for vice president. Earlier this month, Romney's wife, Ann, said her husband was considering choosing a woman as a running mate.
Romney's visit with the GOP sage came as he was in the final stages of picking his No. 2. Cheney is familiar with the process: He was charged with leading Bush's vice presidential search in 2000 and ended up vice president himself. Romney has tasked longtime aide Beth Myers with leading his own vice presidential search.
Cheney has long struggled with cardiovascular disease, suffering a heart attack in 2010, his fifth since the age of 37. Now 71, he received a heart transplant earlier this year at a more advanced age than most patients.
Cheney's daughter Liz also attended Thursday's fundraiser. She recently bought a house in Wyoming, sparking questions about whether she plans to run for office. Her father was elected to six terms as a House member from the state.