Video above: Southwest Airlines flights canceled: Here's how to get a refundMany Southwest customers have been desperately trying something -- anything -- that will get them back home. But some passengers have been horrified to find other airlines posting last-minute flights to their destinations that can cost thousands of dollars.United and American Airlines say they have a solution: The airlines will place price caps on travel to and from select cities, the companies told CNN.Although it didn't specifically mention Southwest, American implied the price caps were designed to help the melted-down airline's customers get home.The price caps vary by location in areas affected by cancellations, an American Airlines spokesperson told CNN. Southwest did not respond to CNN's request for comment.American Airlines notified customers about the price caps in a series of tweets directed at people who posted screenshots of thousand-dollar flights.One traveler posted a screenshot showing flights from San Diego to Orlando with American, Delta and United fares that cost more than $2,000. The passenger was looking to rebook a canceled Southwest flight."We're doing our part to help get people where they need to be and we're putting a cap on fares for select cities," American tweeted.Another tweeted at American Airlines asking for help with delayed flights and no rebooking options (adding in a #southwestdebacle hashtag)."Kindly join us in DMs with the booking code, and we'll be happy to check on available options," American replied.United Airlines also says it is capping fares on some routes served by Southwest Airlines.Video below: Family gets off cruise, learns Southwest flights were canceledThe cap runs through Saturday and applies in many of the U.S. and Latin American markets where Southwest also flies. United spokesman Josh Freed could not immediately specify a dollar amount for the cap."We continue to get people to their destinations as safely and quickly as possible this busy holiday season and our latest effort includes capping fares in select cities to make sure our flights are available to as many customers as possible," Freed told CNN.Cancellations pile upThe price caps could come as a welcome relief for stranded Southwest fliers across the country.Southwest canceled 2,507 flights for Wednesday, by far the most of any airline, according to flight tracker website FlightAware. The airline canceled 2,694 on Tuesday and already has another 2,348 flights canceled for Thursday.Making the travel nightmare worse, Southwest has a policy of not rebooking customers on rival airlines. Southwest Airlines does not have interline agreements with other carriers that would allow its agents to rebook passengers on a different airline, narrowing the options for stranded passengers.Video below: Southwest customers recount troubles caused due to canceled flights"Southwest is unique in the industry in that we don't have codeshare partners," a company spokesman said. "That is just part of our business model."In a video statement on Tuesday, Southwest CEO Bob Jordan spoke to frustrated customers, saying, "I'm truly sorry." Jordan blamed the airline's mass cancellations on record cold temperatures across the country complicating flight paths. "fter days of trying to operate as much of our full schedule across the busy holiday weekend, we reached a decision point to significantly reduce our flying to catch up."Southwest is the largest carrier in the country and the largest airline in 23 out of the 25 top U.S. travel markets, according to the company.