A Lithuanian couple on their honeymoon were among passengers who arrived at Luton Airport in Bedfordshire on Monday morning to find their flight had been cancelled.
Customers due to fly out of the UK with Monarch have been warned not to travel to airports as there will be no further flights.
Vilius Linkunaitis, 31, said he and his new wife, Zivile Rakauskaite, 32, felt "stranded" and "lost" after learning they would not be able to fly.
He said: "We are trying to fly as it's our honeymoon holiday and we are totally screwed at the moment."
The couple, who married just days ago, had flown to London from Riga, Latvia, and were due to travel on to Malaga in Spain for the end of their honeymoon.
They said Monarch was not answering its phones and they could not get through to Kiwi.com, the website operator they booked the flights with.
Mr Linkunaitis said: "We feel very stranded and just lost and I don't know what to do now."
He said they had been told by airport staff to go online to find the cheapest seats on an alternative flight.
Karen Patrick, from Northamptonshire, was due to fly with Monarch Airlines to Rome, Italy, with relatives who are visiting from the United States.
The 53-year-old said fights with alternative operators were "going so quickly" as the group tried to work out what to do.
She said: "We just could not believe it and we have our relatives who have come from America too. It's just unbelievable."
The group only discovered that travel with Monarch had been suspended when they arrived at Luton Airport.
They have managed to get seats on a flight with easyJet on Tuesday and have been forced to pay for the new flights, but hope the cost will be covered by their insurance.
Ms Patrick's cousin, Deborah Bond, 55, from Texas, said: "We are not going to let it ruin our holiday."
Ann Johnson, from Luton, said there had been a lack of information for holidaymakers.
The 75-year-old, who was due to go with her husband on a one-week package holiday to Faro, Portugal, arrived at Luton airport at about 4am on Monday.
She said: "There was no notice up - nothing. We were just walking around looking for the check-in desk."
The couple have been forced to pay approximately Â£450 for two Ryanair flights on Monday evening, including baggage, but face a twelve-hour wait at the airport before take-off.
Ms Johnson said the couple were "angry", adding: "There's no actual information desk here to go and ask anyone and no-one knows what to do.
"There's no-one giving out food or vouchers."
Mark Henson, 50, from Dover, arrived at the airport at 4am for the same flight to Portugal, and was told it had been cancelled.
He said: "We got told to go home: 'We can't help you so you may as well go home.'
"He told me I wouldn't be be able to get a flight."
Mr Henson was able to book two seats on a flight on Monday evening but said it was a "scandal" that prices on other airlines were so high.
He accused companies of "money-making" out of "somebody else's misery".
Mary Quist, 65, booked her holiday to Portugal with Fleetway Travel and was due to fly on Monday morning with Monarch.
She arrived at the airport at around 3.30am and found out her flight was cancelled as she queued for check-in.
She said: "Everyone was standing around, no-one knew what was going on.
"There was no-one manning the Monarch desks and then after a few minutes somebody came out and said 'Very sorry to have to tell you this, but Monarch have gone into liquidation, all flights are cancelled'."
She added: "We were told 'there's nothing we can do, go home'."
Ms Quist, who is from Milton Keynes, said: "We left home at about half past two, kept the radio on all the way down, listened to the news.
"Because the cut-off was midnight they should have known what was going on.
"We just thought we would come down here and carry on.
"I've still not heard anything from Monarch. No email, no text message, nothing from Monarch itself. It's disgusting. Absolutely disgusting."
Ms Quist said she has since been contacted by Fleetway Travel and has been booked on to a flight on Monday evening.