Some couples opt for a traditional wedding, while others go for the Elvis impersonator in Las Vegas. But David Mondrus and Joyce Bayo may be the first to have incorporated Bitcoin.

Before about 50 guests at a Walt Disney World hotel in Florida recently, the couple used a Bitcoin automated teller machine to record their written vows on the currency’s so-called block chain — an open ledger that permanently stores information.

“A diamond is forever, a marriage is forever, but when was the last time anyone looked at their wedding vows?” Mr. Mondrus said. “This technology allows us to get that data and store it in a way that is retrievable and noncorruptible.”

As Bitcoin’s price has declined over the last year, critics have been quick to declare the virtual currency dead. Bitcoin’s true value, though, might be not in the currency itself but in the engine that makes it possible.