CalMac expect more people will attempt to travel on its west coast routes, especially on the Clyde, because of the good weather this weekend.
Property owners have been showing CalMac staff utility bills to try to prove they live on Arran or another island.
One Arran caravan owner said holiday home owners were crossing to the island from Claonaig to Lochranza.
She said: “There are quite a number of these people who have slipped onto the island.
“They should be hunted down and sent packing as they are compromising the safety of the islanders and breaking the lockdown.”
A CalMac spokesperson said: “As has been the case since lockdown began, our staff ask people travelling on all routes if their journey is essential and ask them for proof of either island residency or essential worker status.
“There has always an element of trust and responsibility involved in this and we are following Scottish Government guidelines in that regard.
“CalMac staff hold no enforcement powers and cannot act as the police.
“We continue to ask people to respect the guidelines which state that travel to the islands should be for essential purposes only.”
Director of operations Robert Morrison added: “As the First Minister made very clear yesterday, travel to islands continues to be for essential reasons only.
“They are not open for recreational purposes and people trying to board for a day trip will be turned away.
“Likewise, people with island second homes should not be travelling and we would ask them to be responsible before trying to board.
“The good weather may tempt people to get out and about, but I would urge everyone to continue to follow government guidelines and stay away from the islands.”
Police Scotland Chief Inspector Ian Graham said: "Local officers remain in regular contact with CalMac, which already has procedures in place for ensuring travel is compliant with the restrictions.
"The regulations are clear: people should only leave the house for very limited purposes, for example for basic necessities, for exercise or recreation, for medical needs or travelling for work which cannot be done from home.
"The chief constable has made it clear we are asking people to take personal responsibility to do the right thing and remember the purpose of these measures is to aid the collective effort to protect the NHS and save lives by preventing the virus from spreading.
"Our officers will continue to engage with the public, explain the legislation and guidance and encourage compliance.
“We will use enforcement as a last resort only where there is a clear breach of the legislation.
"We recognise people have made significant sacrifices until now, and while the temptation may be to head straight for one of our beauty spots, we would ask people to use their judgement and avoid going to places which are normally busy during the good weather.
"Complying with the legislation about meeting only one other household outdoors at any one time and following the Scottish Government's guidance about avoiding travelling long distances will stop our parks, beaches, lochs and hills from becoming over-crowded and help ensure appropriate physical distancing is maintained, reducing the spread of coronavirus.”
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