It’s up to the passenger to do the research on the company’s website or phone app to determine the most convenient, time, routing or departure/arrival city. Otherwise, the airline systems will automatically book the passenger on the next available flight on the original route.

Airlines are not obliged to compensate travelers with lodging or meals for delays because of extreme weather.

So in the case of the Ryans, traveling back from Tokyo, Mr. Ryan used the hotel and car rental apps on his phone to estimate the cost of spending an extra day and night in Los Angeles. That made it possible for them to carefully consider their choices.

“On the phone with an agent, we’d have to decide right when they give us our options,” Mr. Ryan said. “Now we can research everything on our time frame — not the airline’s.”

The pair decided to stay in Los Angeles for the day and try a new restaurant they had read about.

That is pretty much how the airlines say they want passengers to respond to weather waivers: by deciding themselves what works best.

“We are trying to put as much control as possible in the hands of customers,” Ross Feinstein, a spokesman for American Airlines, said. The company wants customers to look at alternatives “while they’re still at home, before they come to the airport,” he said.

About a year ago, American updated its phone app with the ability to change itineraries when weather waivers were issued. Mr. Feinstein said that calls to the reservation center during storms had decreased significantly as a result of the new self-serve option.