VATICAN CITY — Sharing lunch is rarely historic, except perhaps when the two people eating are a pope and his predecessor.

On Saturday, the pope emeritus, Benedict XVI — who broke church tradition by resigning rather than dying in office — ate with Pope Francis at Castel Gandolfo, the hilltop villa where Benedict is living, while reporters waited outside for any scraps of news about how the meeting went.

Vatican officials gave no word about what the past and present leaders of the Roman Catholic Church discussed, and even rebuffed questions about what they ate. They did, however, paint a picture of a seamless transition: when Benedict offered his successor the “place of honor” during shared prayers, the Vatican said, Francis demurred, suggesting that they kneel side by side as “brothers.” Their first embrace, a spokesman said, was “wonderful.” Both wore white, the traditional color of the pope’s vestments....