The website advises students to refresh their browser, adding: "We are currently experiencing heavy load on our website. Apologies to all affected. Please try again shortly."
However, an NZQA spokeswoman said the site had not crashed.
"The website has not crashed," she said. "We are experiencing traffic as expected."
The site had seen almost 65,000 unique logins by 12.30pm, NZQA said, as an average of 25,000 students logged in every hour.
Some students have been able to access their results from their school's website instead.
Mt Albert Grammar School student Jaimee McLaughlan said she had been unable to access her results on the NZQA website, so turned to her school's online portal instead.
"At first when I went to look at them the NZQA website was down," she said.
"I went to log in and it was like, 'you cannot go here', so I had to go through the school website. It was a bit of a process.
"It must be everyone's on it at the same time, frantically."
McLaughlan got the results she needed to get into her courses for Year 13, but was disappointed she had not gained excellences in some of her subjects. She sat Level 2 physics, chemistry, calculus, English, dance and design.
"Half of it I'm very happy with, and others I'm very disappointed.
"Some of the ones I was very confident with I didn't get the marks that I was looking for, so that's a little bit annoying.
"But I'll just check my papers and hopefully be able to send them back or see where I went wrong."
She added: "Sometimes you make silly mistakes that you can't see at the time."
She would consider seeking a review of her results, she said, but would check with her teachers once her test papers were returned. Exam answer booklets should be returned to students by mid-February, NZQA said.
"The ones I was struggling with, like my English, I was very happy with those results, which is a bonus.
"It's always the way: the ones that you feel worse about you do better on than the ones that you feel super confident with.
"But I'm still happy with how they went, I still passed everything which is awesome."
Fellow Mt Albert Grammar student Isaac Munro, 16, said he was able to access his results on the school's website last night.
Most of Munro's friends had also done well, he said, however a few were still waiting to logged into the NZQA website.
Rulon Brown, who is going into Year 12 at Otahuhu College, is celebrating getting all his Level 1 subjects endorsed with excellence. He sat English, mathematics, music, drama and geography.
"I got Level 1 endorsed with excellence, for the whole thing. I have three individual course endorsements - two at merit and one at excellence."
He was "pretty chuffed", he said.
"It feels good to know that after working hard and preparing things the results are good.
"I'm looking forward to another year of working hard, keeping it consistent."
Brown believed his parents would be "happy, proud parents" when they found out his results.
Ella Vukovich told the Herald she escaped the website madness by getting her results last night.
"We logged on to our school website early yesterday and the marks had already been released! The NZQA website has crashed so we got very lucky!"
An NZQA spokeswoman said it was not unusual for some schools to have access to results before they're officially released by NZQA.
"Students have access to school management systems and therefore some are able to view some results overnight. This is not an error or mistake," she said.
"Schools have access to student results so that they are able to assist them with queries and have discussions about subject changes or new enrolments. This is standard practice, and has been for some time."