All the while, their mantra was “respectful engagement,” with a side of “tranquilo.”

With Schwechheimer were a Rhode Island financier, a university professor of sports management, a veteran minor league executive, and three members of the Cohen Group, a high-voltage consultancy firm in Washington: Tommy Goodman, a Spanish-fluent lawyer who handled the trip’s every detail, and two legendary American statesmen.

One, Marc Grossman, a former ambassador to Turkey, retired in 2005 as the State Department’s third-ranking official, serving as the undersecretary of state for political affairs. In 2011, Obama called the retired Grossman into temporary service as a special representative for Afghanistan and Pakistan.

He roots for the Los Angeles Dodgers.

The other, Jeffrey Davidow, has been the ambassador to Mexico, Venezuela and Zambia, as well as the assistant secretary of state for Western Hemisphere affairs. He retired in 2003 as career ambassador, the Foreign Service’s highest position, which, by law, can be held by no more than five people at a time.

He follows the Boston Red Sox.

An Emphasis on Patience

The two Foreign Service veterans had learned long ago how to hear what was not being said, how to deconstruct a handshake, how to deftly use the tool of time. They understood the value of patience.

For example, on the group’s first night in Havana, Schwechheimer treated several Cuban friends to dinner. He mentioned in passing that he would someday like to share his baseball plans with Antonio Castro, an orthopedic surgeon, one of the country’s most prominent baseball officials — and a son of Fidel.

It was quickly intimated that such a meeting was possible. The next night, one of Schwechheimer’s dinner guests, a former Cuban legislator, invited the Americans to the historic Hotel Nacional de Cuba. There they were introduced with some pomp to the hotel’s manager, who said he would provide a private room for the meeting on the day it happened.

Then the American entourage was led into a small theater to watch a long cabaret performance that seemed lifted from a 1940s MGM musical. Every so often the legislator would raise his hand, and bottles of Cristal beer, bowls of olives and trays of cured ham would appear.