Around TV sets from Baltimore to San Diego yesterday, they kept the gut-wrenching vigil once more. But this time, before they heard the crucial official word, many of the families of the American hostages had broken out the chilled champagne and dared to believe.

In Memphis, Ernest and Susan Cooke, parents of hostage Donald Cooke, laid out a feast of cold cuts and cheese for the reporters and cameramen who swarmed to their home. A bottle of champagne sat chilled and ready on the patio.

"We're allowing this [invasion] only because we're assuming it's going to be good news," said Cooke, a professor of marketing. "I've got butterflies all over," said his wife.

Across the continent in San Diego Dorothea Morefield, wife of hostage Richard Morefield, set out half a dozen champagne glasses in her living room while 40 reporters watched. She popped a turkey -- which had been put aside and frozen to await her husband's return -- into the oven in the kitchen. As one family member said, it was "a thanksgiving turkey."

"There's still that little voice in the back of my head that says, 'Don't believe this. Don't jump up and down,'" Morefield said. "But I believe it."

By lunchtime yesterday she had organized a pool among the reporters, taking bets on what hour the plane carrying the hostages would lift off from Tehran.

In Passadena, the Rev. Earl Lee, father of a hostage, prayed before his congregation that the captives will "leave all hatred and all resentment . . . may their hearts be swept clean," as they board their plane to freedom. In this prayer before 1,800 parishioners at the First Nazarene Church, which was festooned with yellow ribbons, he also included a word for President Carter: "May he sense the love of the people."

Lee, the father of hostage Gary Lee, said as he left the church that yesterday was "the best day" he has had since the 14-month ordeal began.

Pat Lee, the hostage's wife, lives in Falls Church with their 10-year-old daughter, Dana. The two of them were "running back and forth between the television and the radio" for news, according to a family friend, as information oozed out with agonizing slowness through the day and into the night.

Pat Lee was "amazingly cool," the friend said, but like many hostage family member, had decided not to speak to the press until the crisis had ended "because there have been so many disappointments in the past."

In the small-town intimacy of Globe, Ariz., hostage Marine Sgt. Jimmy Lopez seemed to become the missing son of the whole community as the first word of a breakthrough came during Sunday mass. It came from a network TV crew asked out at Holy Angels' Church, where the Lopez family was attending services.

"An international event has become a personal experience in this small town," said the Rev. Charles Maloney, pastor of the church and an unofficial spokesman for the family, "There's that anxiety; it's a part of history we're living right here.

"No one's that excited yet," he added. "Everyone's taking the attitude of the Lopez family. They'll believe it when they see the hostages actually step off the plane."

Outside the church, Mary Lopez told reporters: "I don't know whether to laugh or cry right now. I suppose I could do both."

"I feel like a scenic railroad going up and down," said John Smith of Rising Sun, Ind., stepfather of hostage Don A. Sharer. "We try not to get up, because these crazy people can do anything at the last minute. But . . . we're up."

Doris Moeller, of Loup City, Neb., the mother of hostage Marine Staff Sgt. Michael Moeller, burst into tears when she answered the phone and a reporter told her about the official optimism that the hostages might be released soon. She had been trying not to get "too keyed up," she said, "because I can't come down anymore."

As the end seemed in sight, relatives of some of the hostages turned their thoughts beyond the emotions of the moment to the possible of all of this on them and their captive loved ones.

The State Department's arrangements for the families' reunion with the hostages "in an undisclosed location, was a direct request of the families," said Katherine Keough, wife of hostages William F. Keough Jr. and leader of the families' organization. "We think most of the media will be responsible, and recognize that this is a personal moment."

Yesterday afternoon Carter called Keough, president of the Family Liaison Action Group, and the group's spokesman, Louisa Kennedy. They were on the seventh floor of the State Department, keeping track of developments.

The president "made us feel very good," Kennedy said. She is the wife of hostage Moorhead Kennedy.

And at New York's St. Patrick's Cathedral, Cardinal Terence Cooke conducted a special prayer service for the hostages. Former hostage Richard Queen was in the congregation.

Betsy Morefield, 22, a graduate student at the University of Virginia at Charlottesville and the daughter of hostage Morefield, spent an anxious day in her apartment looking ahead.

"You know," she mused, "the person getting off that plane won't be the same person who got on a plane 14 months ago. The people waiting to greet them aren't the same people who put them on the plane. We've got to be aware of that.

"We may be ending one part of this [ordeal]. But we're beginning another."