MOST PASSENGERS holding tickets on Braniff flights when the airline suddenly shut down May 12 appear to have weathered the crisis in their travel plans with a minimum of delay and little or no loss of money.

"There was a blip in the service, but we didn't see nearly the grief factor caused by the Laker demise," says David Stamey, managing director of the International Airline Passengers Association in Dallas, where Braniff was headquartered. (Laker Airways, the cut-rate British airline, went out of business Feb. 5, stranding 40,000 ticket-holders.)

While thousands of Braniff ticket-holders flooded the Civil Aeronautic Board's consumer hotline with inquiries, most were able to be accommodated by other airlines because of mandated or voluntary actions aimed at protecting passengers, says Hoyte Decker, assistant director of CAB's consumer affairs office.

"I'm guessing that the vast majority who held tickets and desired to travel were flown," says Decker, who had not compiled statistics on the exact number of calls received.

Those who held tickets on a Braniff flight issued by a travel agent or another airline were assured of travel without extra cost because of inter-airline agreements approved by the CAB. More at risk were passengers who held tickets on Braniff issued by Braniff. In most cases, say Decker and Stamey, other airlines flying the same routes volunteered to honor the tickets, though they may have imposed time limits or required stand-by status.

Despite the safeguards, some unlucky travelers did lose out. Among them was a young Frenchman anxious to get home. When he contacted the CAB, he had only $50 in his pockets. He held a Braniff-issued ticket for a return flight from New York City to Paris, but had been unable to locate an airline that would take him.

His problem was an unusual one, explains Decker, in that his ticket was "open"--it did not specify an airline or a flight. If a specific airline had been named, his chances for a flight would have been much better, since carriers have been honoring Braniff tickets involving their flights. The CAB could only direct him to the French consulate.

Other potential losers were business travelers who could not risk standby status required by a substitute airline because of an important meeting and who, as a result, purchased a second ticket to insure a seat. For a refund on the Braniff ticket, they will have to apply to the bankruptcy court in Dallas, which does not insure a full return. Holders of Braniff-issued tickets who decide to cancel a planned flight would also have to file for a refund.

Delays and other inconvenience were more common, at least the first couple of days after the Braniff announcement, says Decker, when passengers had to scramble to get on alternate flights. Many had to reroute their trips or take a flight with one or more stops instead of a nonstop.

As outlined by the CAB, tickets issued by a travel agency are protected by the Default Protection Plan, which was originated by the carriers and approved by the CAB on April 15. Under the plan, the airlines have agreed to transport passengers at no additional charge, though they may set such conditions as standby status. They are not obligated to make refunds for cancelled trips.

If the ticket was purchased from an airline other than Braniff (with a Braniff flight involved), passengers have the least problem. In such a situation, the issuing airline retains the price paid for the ticket until the Braniff flight is completed. Since that won't happen, the money can be transferred to another airline or refunded at the passenger's option.

One other factor came into play on international flights. When the CAB awarded Braniff's international routes to other airlines following the shutdown, it required them to honor Braniff tickets. CAB approval was not required when other airlines stepped in to take over Braniff's domestic routes, says Decker. However, most are honoring Braniff tickets, with some restrictions, as a public relations gesture.

Passengers with problems may call the permanent CAB consumer hotline, 673-6047. For those who have a Braniff ticket they are unable to use, refund claims can be filed from: The Honorable John C. Flowers, U.S. Bankruptcy Court, Northern District of Texas, 10th Street and Lamar, Room 206, Fort Worth, Texas 76102. Cite Braniff case no. 482-000369.