But as soon as Mr Martinovich got out of the driver's seat and started walking towards him, Mr Hamilton knew something was wrong.
"I just saw the look on his face and the way he was looking at me and he was excited-slash-panicked. He said, 'Mate we are having a baby'."
Mum, baby and Mr Hamilton were reunited yesterday at Waikato Hospital following the birth of the Martinovichs' fourth child.
Recalling Monday's action, Mr Hamilton said it was not unusual for speeding motorists to concoct a story about racing their pregnant wife to hospital to avoid a ticket. But in this case, "I looked through the window and saw [Mrs Martinovich] and instantly knew".
Heavily pregnant, she was groaning in the front seat.
Not keen to learn the art of midwifery then and there, Mr Hamilton offered to call an ambulance or take them to the closest birthing centre in Te Awamutu.
But because the baby was four weeks early, their midwife had instructed the dairy farming couple, who had moved to the Waikato from Whangarei that week, to meet her at Waikato Hospital.
The journey from the couple's home would usually take 55 minutes but they had no idea how to get there and in their rush hadn't even packed an overnight bag.
"My initial plan of action was to get [Mrs Martinovich] inside my car and go from there," Mr Hamilton said yesterday. "But she couldn't move so on to plan B which is to follow me. So lights and sirens all the way from Te Kawa right into Hamilton."
Mrs Martinovich said it turned out to be a good thing they were pulled over.
The heavy traffic cleared when people heard the police sirens and the couple would have got lost without Mr Hamilton showing them the way. She thought her daughter may have been born at traffic lights if they hadn't been escorted.
The helpful police officer escorted the anxious couple right to the doors of the delivery suite and he was even summoned to grab a wheelchair to help Mrs Martinovich in, which he joked was all part of the service.
Mrs Martinovich's waters broke as she got out of the vehicle, at which point her husband walked over to the officer with his driver's licence.
"I said, 'We won't worry about that now my friend, you go have a baby'," Mr Hamilton said.
The policeman headed back to work, but got a call from Mr Martinovich five minutes before his shift was due to end, sharing the good news.
Within 25 minutes of arriving at the hospital, Kyla Lucy Martinovich was born weighing a healthy 3.5kg, despite being premature.
Mrs Martinovich said the couple were a bit flustered having only unpacked their belongings into their new house the day before, and did not yet have baby clothes ready for their fourth child, whose due date was July 2.
Her sleeping baby daughter charmed Mr Hamilton yesterday with her impressive coverage of black hair and chubby cheeks. She is being kept in the hospital's Neonatal Intensive Care Unit so her low blood sugar levels can be monitored.
The couple's three other children, Abbey, 13, Ryan, 11, and Brady, 3, are waiting to meet their little sister whose early arrival has even helped them have a few days off starting their new school.
Meanwhile, the highway cop who helped make sure the newest family member was brought into the world safely and her very grateful parents have swapped phone numbers and hope to keep in touch.
