Cats particularly needed to be kept indoors, as if an evacuation was ordered, it could be hard to find them at short notice.
"Get a pet carrier for each small animal, whether it's a cat or a rabbit, because when you go to the vet you typically only take one animal," Glassey said.
"But if you evacuate you'll have to take them all.
"So having a pet carrier for each animal is a really important part of evacuating small animals."
Precautions such as stocking up on extra food was a good idea.
"With power loss, animals that rely on environmentally controlled accommodation, such as tropical fish, can be in trouble," Glassey said.
"Make sure you've got means, whether it's a generator or something else, to keep them at the temperature they need to be at."
Outside of the immediate physical risks, animals could also become stressed and anxious in a storm.
"Keeping them together as a family unit to look after one another is always a nice thing to do."
Glassey said microchipping became particularly important in severe weather, as any frightened animals that ran away could be reunited with their owners very quickly.
Anyone who finds a stray animal after the storm should take it to the local vet or SPCA, as well as putting a post on www.petsonthenet.co.nz.
Horse owners and those in rural areas, are being told to move their animals to higher ground.
If flooding occurs, move the animals out of floodwaters as soon as it's safe to do so, as contaminated water can cause bacterial infections or chemical burns.
Check any large outside animals for injuries following the storm, as fright may cause them to run or swim through fences.