Worried about missing what seemed to be a looming deadline to get back home, we started looking for new tickets — without having canceled the old ones. It was immediately obvious that, less than an hour after Mr. Trump’s pronouncement, swarms of other anxious travelers were trying to do the same thing. We’d click on an airfare, only to find it was “no longer available.” It was like trying to catch a firefly that hovered before you for a moment and then winked out before you could grab it.

What was left were increasingly oddball flights — 31-hour treks on airlines we’d never heard of — and a smattering of very expensive ones. Same-day economy tickets from Paris to New York appeared for thousands of dollars apiece. Because my credit card’s travel benefit has a 24-hour cancellation policy, I took the plunge and used it to buy two basic one-way tickets that, combined, cost more than $5,000. We rationalized the cost by figuring if we were eventually able to get a better deal by changing our original tickets, we could still get our money back for these new ones.

No sooner did I hit the “purchase” button than an update appeared on CNN: President Trump’s travel ban did not cover Americans in Europe after all, only foreign nationals. Whipsawed, we scrambled to cancel the tickets we had just bought — and quickly found it impossible. Cancellation options online were either unavailable or did not work, and the airline’s wait time for callers was now up to six hours. And my credit card customer service line played music for two hours before disconnecting.

We decided on one last play: Get to the airport and try to cancel, in person, through a ticket agent. We packed up, assuming that if our scheme didn’t work, we’d have to decide on the spot whether to take the flight and be done with it. A 45-minute Uber ride later, we were at Charles de Gaulle Airport, staring at an impossibly long line of passengers beseeching harried ticket agents for help. It was obvious that in the hours it would take to finally reach the customer service counter, our flight would have already left.