The people responsible could face charges of wasting police time, but it was unlikely the woman who radioed the coastguard would be found.
Coastguard duty officer Mark Leevers said the woman's story was credible and she had given near-exact details of her location.
"The scenario she was describing was such that it led us to believe there was somebody in real difficulty and in urgent need of assistance. We spent two hours searching for them before we established the call was a hoax.
"It was extremely frustrating considering the amount of resources we put into trying to find and rescue these people."
Mr Leevers estimated the cost to be around $20,000.
Marine police and the Eagle helicopter joined the search, as did the Auckland Westpac Rescue Helicopter and the Harbourmaster. Boaties in the area also assisted.
Inspector Mark Hall, who oversees the operation of the Eagle, said hoax callers were "idiots".
"It potentially takes away resources that could be used elsewhere or for some other emergency," he said.
Mr Hall said it was difficult to locate the origin of marine radio calls but if the person was identified, they could be charged with wasting police time "among other things".
A helicopter expert said the Eagle was likely to burn around 220 litres of fuel and cost upward of $2200 an hour.
Police said they had identified the person who made the bomb hoax call.
"It was a considerable waste of police time and resources and a lot of emergency services' time," Counties Manukau police spokeswoman Natalie Swart said.
The passenger had been unaware of any bomb threat and would not be charged, but he had been sent back to New Zealand because of an unrelated immigration issue.
"We are confident he was not privy to or involved in this hoax call."