She described the birth as "a heartwarming occasion in uncertain times".
"I'm so proud of our crew, who have shown commitment to keeping services to Waiheke going throughout level four, and this exceptional event in challenging times will be another sailing to remember," she said.
The birth is the second baby born on board a sailing from Waiheke in the past six months.
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"Our people are trained to provide assistance and support in situations like this, and we are proud of how they responded and supported our passenger, and her midwife, during this time," said Watson.
The essential service between Waiheke and Auckland has been running hourly with a passenger register in place to assist with contact tracing, and to monitor essential travel.
The service will continue throughout alert level three with the same precautionary measures in place that have been in place at alert level four.
• Covid19.govt.nz: The Government's official Covid-19 advisory website