Dedicated sites to swab possible COVID-19 patients are starting to get up and running.
But concerns remain about the criteria for testing and whether there is access to enough equipment to do it.
Kiwis rushing back across the border are subjected to questions about their health and offered advice.
Border officials are telling arrivals to stay away from others and call Healthline immediately if they get sick.
If you call Healthline you could end up being referred for testing at one of the dedicated COVID-19 clinics across the country.
But you can only turn up if you've been referred and fit certain criteria, including a fever or sore throat, shortness of breath or cough and have been overseas.
You also fit the criteria if you any of those symptoms and had contact with a probable or confirmed case.
GPs can also use their own judgement and do a test if they want to.
The National Party health spokesperson Michael Woodhouse says we need to be testing more.
"We need to do more of it. And those countries that have, have managed to reduce the amount of community transmission," he told Newshub.
"We need to be testing far more Kiwis than we currently are."
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A resident in Invercargill who was sic and did have contact with a confirmed case told Newshub she was told by staff at her medical clinic she didn't qualify for a test.
When she insisted she was then told the clinic only had five swabs left. She eventually got the test in the clinic's carpark, but only after she complained to the Health Ministry.
And a Christchurch GP told Newshub that "there aren't enough swab kits in Canterbury for us to do them. We've rung the lab asking for more but they are being rationed."
Director-General of Health Dr Ashley Bloomfield has said there is enough to go around.
"We don't have a shortage of swabs at the moment. We are just making sure that we can continue to have both the swabs and other supplies needed to keep testing everybody who needs to be tested."
With the mass exodus from overseas underway, the number of tests needed will only increase.