Callers who contacted UTV indicated that trains were too packed to stop at stations in Coleraine and Ballymoney.
But bus and train operator Translink asked people to be patient.
A Translink spokesman said: "Due to the large scale of this even and the amount of people visiting Belfast, we have every available bus and train in service."
The company said it has made all of its trains and buses available and insisted its services were now running more smoothly.
The problems arose as tall ships from across the world arrived in Belfast, to end the historic transatlantic race in the city's quayside.
'Biggest event'
Tens of thousands of visitors arrived in Belfast on Thursday to see the Tall Ships fleet.
Forty vessels tied up their main sails and dropped anchor at the quayside to begin a four-day visit.
With the rain holding off, tourists and locals alike flocked to the regenerated dockside to step aboard for a look round the impressive triple-masted boats, which hail from as far afield as Uruguay and Brazil.
"This will be the biggest event that Belfast has ever hosted and the single biggest event on this island this year," said Lord Mayor Naomi Long.
"We will have visitors from all over the world and they will enjoy the warmth and hospitality for which Belfast people are renowned."
A number of young people from Northern Ireland crewed one of the boats - the Europa - on the ocean trip.
Leanne Kingston, 18, from Belfast, said it was the experience of a lifetime.
"We all stuck together and looked out for each other and made sure we were all okay," she said.
"Coming through the storms people think it would be really scary, but it was really fun, clinging to the sides and clinging to each other trying not to fall over. Half of us are covered in bruises from head to toe but we don't care because we had a good time anyway."
Belfast beat off competition from other European cities to win the right to welcome the fleet after its final leg.
Nearly half a million people are expected to descend on the city for a glimpse of the huge wooden boats during the four-day Tall Ships festival.
'Image boost'
Around a dozen of the ships completed the race across the Atlantic with the rest joining up with the fleet for the final port of call.
They are open to the public to visit from Thursday, before sailing out of the docks in a convoy parade on Sunday.
The festival, which the city council estimates will generate £10m for the local economy, also consists of a range of free activities and entertainment, including fireworks, continental markets, funfairs and concerts, all based around the docks area.
Belfast Mayor Naomi Long said the event represented a real investment for Northern Ireland.
"Belfast City Council is the single biggest investor in this, but the return has been enormous. It's good for tourism, it's good for our image abroad," she said.
"It's also good in terms of infrastructure development, so that we'll be attract other events to Belfast."
Chair of Belfast's Tall Ships board, Dr Gerard O'Hare, said the redevelopment work at the docks would leave a lasting legacy.
"Looking around the Port of Belfast today and seeing this fantastic transformation makes me very proud and we hope that the hundreds of thousands of visitors enjoy this special experience," he said.
The last Tall Ships Atlantic Challenge race was nine years ago and the only other occasion the ships visited Belfast was in 1991.
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