Lancaster Royal Grammar School and Dallas Road Primary School have both been forced to keep certain classes off school as a precaution.
At LRGS, around 50 students from the Lower Sixth were sent home after a pupil had a positive test result despite showing no symptoms.
They have now returned to lessons.
Principal Dr Chris Pyle said: "Last Friday we were notified that one of our students had received a positive test result. He had no symptoms but following the government guidance he had been self-isolating at home after one of his family members tested positive.
"As a precautionary measure, and following our risk assessments, we sent about 50 students from his classes home while we waited for external advice.
"Public Health England later confirmed that they were not at risk and there was no need for them to isolate, because the student had already been self-isolating for an extended period and had not been in school. Students then returned to lessons.
"Just one positive test result in a school has the potential to cause huge disruption, and this case was a reminder of how important it is to self-isolate immediately if anyone in your household has possible symptoms."
At Dallas Road, head Phil Wright took precautions after a positive test result in a Year 2 class.
In a letter to parents he said: "As a school we continue to follow the guidance we are given and work hard to ensure that we provide a safe and vibrant environment for your child/ren.
"All staff and children needing to isolate as a result of a positive test are now isolating.
"This time of year, even in non-Covid times, is always a challenge as children and staff begin to share coughs and colds brought on by the changing weather.
"It becomes difficult to know what is best in terms of sending children into school. This is even more difficult at the moment when there is heightened awareness surrounding coughing.
"We trust that parents know their children best and are confident that the symptoms the children show are ‘seasonal sniffles’ rather than Covid. However, if we think the child is symptomatic, we will directly ask parents to collect their child and book a test."
Mr Wright also thanked parents for the "overwhelming support" shown in response to their need to isolate the children.
"Your trust, understanding and appreciation have been invaluable, particularly when it comes to avoiding rumours and speculation," he said.
Meanwhile, a nursery in Lancaster closed to two-year-old pupils after several members of staff showed symptoms of coronavirus.
Appletree Nursery, in Milking Stile Lane, said it was a precautionary measure and that no members of staff had tested positive for the virus.
The nursery is awaiting test results for those members of staff who were showing symptoms and said that three-year-olds are still able to attend.
A statement from the nursery said: "In recent days some of our staff team at Appletree Nursery School have developed symptoms associated with Covid-19 and are awaiting results from being tested. I'd like to reassure you that we currently do not have any positive cases of coronavirus within school.
"To minimise the risk of having an outbreak in school, we have made the decision to close the Apple Blossoms Room, the "bubble" where we look after our 2 year olds.
"For safety, we cannot move staff between bubbles, therefore we will still remain open for our 3 year olds and will only reopen Apple Blossoms when test results are known and staff are well enough to return to work.
"I apologise for any inconvenience that this may cause you and thank you for your patience and understanding in the meantime."