A man was arrested allegedly trying to cross the border at Corowa on Wednesday and three others were turned away at major checkpoints.
A 34-year-old from Victoria allegedly attempted to drive in NSW along Carlyle Road just after 11am, telling police he intended to cross the border despite not having a valid exemption.
He was arrested and taken to Albury police station to assist police with their inquiries, while his wife and three children complied with police direction and returned to Victoria.
Three Melbourne drivers were also caught at different checkpoints as police examined permits in the hours after the border was closed at midnight.
Two men were charged for allegedly possessing the drugs GHB, methylamphetamine, buprenorphine and steroids plus two knives and $4065 cash as they crossed the border into Tocumwal on Wednesday.
The 24-year-old man from Queensland driving a Victorian registered car and his 28-year-old male passenger from Tocumwal, who appeared to be drug-affected, were refused bail and will appear at Albury Local Court on Thursday.
NSW Police Commissioner Mick Fuller said the experience of permit checks had been "a positive one" with the exception of those turned back.
"Some vehicles have been turned around, sent back to Victoria, because the drivers came from postcodes that are of threat from the virus," he said.
"Outside of that, the permit system is working and thousands of vehicles have been able to travel.
"Most of those have been either heavy transport or people travelling in those border town bubbles."
He warned driver that highway patrol and other police would be checking any cars with Victorian number plates outside of of Albury and on-the-spot-fines could be issued.
NSW Police Assistant Commissioner Scott Whyte was in Albury for the border operation on Wednesday and dismissed criticism - including from mayors Kevin Mack and Anna Speedie - that the checkpoints were not working because of the delays.
He rejected a suggestion permits would not be checked during peak hour.
"We are enforcing the NSW health order and we will continue to do so," he said.
"It's been a very large task and it wouldn't have been achievable without the input of the local community - local councils and other local services assisting us."