“Are you ready for a great flight? So are we.”

The Southwest Airlines poster in a San Diego International Airport jetway wasn’t created to herald the airline’s return to normal over the weekend.

But those words hit differently after the airline’s holiday travel meltdown, a serious hit to its sterling reputation.

Are Southwest passengers, a famously loyal bunch, ready to forgive the cancellations that stranded travelers and baggage across the country around Christmas? And what steps must the carrier take to win back their trust?

The airline’s long road to recovery got off to a smooth start over the weekend. Southwest canceled fewer than 100 flights combined on Friday and Saturday, according to FlightAware. From Monday through Friday last week, daily cancellations topped 2,300 as the airline slashed its schedule in a bid to fix its operation.

Despite a 90-minute weather delay, the mood aboard Southwest Flight 867 from San Francisco to Las Vegas Friday night was celebratory, empty seats nonexistent. The pilot apologized to passengers for what he described as the trouble this week. “Thanks for giving us another chance,” a Southwest flight attendant said when the flight landed. 

Cancellations stranded baggage in airports such as William P. Hobby Airport in Houston around Christmas.

Photo: Brandon Bell/Getty Images

The biggest tests facing the nation’s largest domestic carrier by passengers lie in the weeks and months ahead. Transportation Secretary Pete Buttigieg put the airline on notice and Democratic lawmakers want answers, too, scrutiny the airline will need to address. Replacing balky crew scheduling technology, which Southwest blames for its severe lag in rebounding from bad weather, will likely also move up the list of the company’s priorities. 

The most immediate question: How far will Southwest go to do right by passengers seeking reimbursement and other compensation for their travel trouble? It has repeatedly pledged to cover all reasonable expenses, including flights, hotels, car rentals and other costs incurred by those whose travel plans were messed up, some repeatedly.

Southwest has refused to publicly define reasonable, arguing that individual circumstances vary widely. That leaves a lot of room for interpretation—and potential for stinginess and bureaucracy. Anyone who has ever submitted receipts for a lost or delayed bag on any airline knows resolving it can be as painful as an IRS audit.

Southwest has already posted links to reimbursement forms on its website, displaying the information prominently.

“We want to take care of our customers who were disrupted, and our desire is to begin to restore their confidence in Southwest Airlines as quickly as possible,” Southwest Chief Executive Bob Jordan said in a memo to employees late Friday.

Southwest rarely misses an opportunity to brag about what it calls customer-friendly policies. But free bags and flexible change rules aren’t on travelers’ minds after this fiasco. It’s trust. I’ve spoken with and heard from dozens of Southwest passengers over the past week who can’t fathom how things went so poorly for so long. The common theme: What happened to Southwest?

Southwest spent decades building one of the most loyal followings of any airline. Many people don’t just fly Southwest, they love it. Doing more is about getting that love affair back with their most loyal customers who helped make the airline in the first place. 

I’d argue the airline needs to do more than refund ticket prices and reimburse passengers for reasonable expenses if it wants to restore the reputation and customer-satisfaction scores it treasures more than anything. 

Southwest needs to open the vault, regardless of the short-term price tag. The airline that rails against airlines that nickel and dime passengers should be liberal in approving expenses.

And it should go above and beyond with its signals of goodwill. I took four Southwest flights in the western U.S. on Friday and was surprised by the lack of welcome back gestures such as free drinks or in-flight Wi-Fi.

For frequent fliers, Southwest needs to do more than extend the qualification period for elite status, which it announced last week. Bonus frequent-flier points would be a start.

Southwest regularly issues travel vouchers when things go awry. It calls them LUV vouchers and they differ from travel credits issued in lieu of a refund. Southwest generously handed them out when it had what would now be called a mini-meltdown in October 2021. I received a $250 LUV voucher at the time for a flight cancellation that in hindsight was a minor inconvenience.

With Southwest stranding passengers for days this holiday season, it should be doling out those vouchers like candy.

Write to Dawn Gilbertson at dawn.gilbertson@wsj.com