"I frankly hold Dick Cheney in really high regard in his role as vice president and as an American," Pence said in an interview on ABC's "This Week" that was taped on Saturday and aired on Sunday.
"Vice President Cheney had experience in Congress as I do and he was very active in working with members of the House and the Senate," Pence said.
Cheney, vice president to Republican George W. Bush, was known for wielding strong influence in the administration, particularly in Bush's first term. Cheney was a forceful advocate of the decision to invade Iraq and some aides to Bush have said they believed he wielded too much power.
Pence said he had spoken with Trump about areas he would focus on as vice president but said he did not want to discuss their private conversations.
Cheney has said he will support Trump in the Nov. 8 election against Democrat Hillary Clinton.