Donald J. Trump met with Gov. Mike Pence of Indiana on Saturday at one of Mr. Trump’s golf courses in New Jersey, as he sizes up potential running mates before the Republican National Convention this month.

The meeting, initially expected on Friday evening, took place on Saturday morning at Trump National Golf Club in Bedminster, N.J., according to four people briefed on the get-together who requested anonymity because they were not authorized to speak about it.

Mr. Pence’s wife, Karen, was at the meeting, but Paul Manafort, the Trump campaign’s chief strategist who has been handling much of the search for a vice-presidential nominee, was not, two of the people briefed said.