The Deputy First Minister said the Scottish Government wants people to take the “very reliable” tests more frequently.
From Monday, proof of a negative coronavirus test will enable entry into venues subject to the vaccine passport scheme.
Mr Swinney spoke to the BBC’s Good Morning Scotland radio programme on Monday, saying there is now a “high level of vaccination in society”, meaning there can be more flexibility around the rules for entry into places like nightclubs.
He said: “We want people to increase the frequency of the use of lateral flow tests, away from the two times per week to much more frequently when they are socialising and interacting with others.
“Personally I am now doing a lateral flow test every day I am going out with the prospect of meeting other members of the public outside my household.”
Mr Swinney added: “I would encourage others to do exactly the same, because that gives me confidence I’m protecting my household and it gives me confidence I’m protecting other people.”
The Scottish Government currently encourages people to take lateral flow tests twice a week and whenever they plan to meet people.
Mr Swinney was also asked about the reliability of the self-reporting system for lateral flow tests.
He said: “We’ve got to ensure that people are participating in a serious fashion with this measure.
“The lateral flow tests are very reliable tests.
“We estimate in different stages there’s 80 per cent to 90 per cent accuracy in lateral flow device tests.
“So they are a source of authority on whether individuals have the virus, so it’s important that people engage with this seriously.”
He continued: “It’s in nobody’s interest, absolutely nobody’s interest, for people not to take this seriously.”
From 5am on Monday, people have been able to show a record of a negative test – either from a lateral flow device (LFD) or PCR – in the past 24 hours to gain entry as alternative to proof of vaccination.