Serco NorthLink sailings were expected to resume on Sunday evening with the departure of the Hjaltland from Aberdeen between 8pm and midnight.
The ferry company said there would be no stop at Kirkwall. The vessel would head straight for Lerwick where she was likely to arrive sometime on Monday morning.
The Hrossey, which has been stuck in Lerwick for several days, was expected to leave on Monday morning at 7.30am and arrive in Aberdeen at 8pm on Christmas Eve.
Serco NorthLink managing director Stuart Garrett said the disruptions over the weekend had been “hugely disappointing” for people hoping to travel for the festive season. However, the company’s priority was the safety of its passengers and crew and they would not sail unless it is safe to do so.
Mr Garrett said: “We have been watching weather forecasts closely and are optimistic we will soon be able to resume services. Our aim is to ensure as many people as possible get home for Christmas.”