Gibian was told there was no refund but he could get a credit on a future cruise.
Passengers on the current cruise disembark in Auckland on Saturday and the couple is worried new passengers will board oblivious to situation.
In a statement, Celebrity Cruises said people affected by the illness were being treated by the ship's doctors and responding well.
The company said the cases were "a reflection of the numerous reports of such illnesses in the community in recent months".
Celebrity Cruises said they sent a text message informing passengers boarding had been delayed so staff could do more cleaning and sanitisation of the ship due to cases of illness.
Passengers booked on the next Celebrity Solstice cruise due to leave Auckland on Saturday would be given the same advice and more crew, including housekeeping and medical staff, were being added to help with the comprehensive sanitation programme, the statement said.
Celebrity Cruises said it was taking a number of actions to prevent further contamination, including covering buffets, providing hand sanitiser around the ship and cleaning and sanitising the ship when guests embarked for the day and at its home ports in Sydney and Auckland. It was following advice from health experts that the best defence against stomach viruses was to wash hands and educating passengers about this.
How norovirus spreads:
• Consuming contaminated food or drinks
• Touching contaminated surfaces or objects and then putting your fingers in your mouth
• Having direct contact with an infected person - for example by sharing food or eating from the same plate or cutlery
• Through the air when vomiting sends tiny particles into the air
Symptoms:
• Nausea
• Vomiting and diarrhoea
• Stomach cramps
• Headache
• Low-grade fever
• Chills
• Muscle aches
Treatment:
• Drink plenty of fluids such as plain water and oral rehydration drinks
• Don't take medicine to stop vomiting or diarrhoea
Source: Ministry of Health