There are only two ways to get from the North to the South Island and that is by air, done that hundreds of times, and by sea.
Years ago there was a vehicle ferry that went from Wellington to Christchurch but now the sea link (for vehicle transport) is just Picton (in the south) to Wellington (in the north).
At its narrowest point the gap between the two islands is not especially wide but the ferry journey is over 100km (according to Mr Google). Because of the geography the winds between the two islands can be fearsome with very uncomfortable ferry crossings . Fortunately on all five of my crossings the weather gods have been smiling on me.
The exit from Queen Charlotte Sound, a sharp turn for the ferry and requiring considerable skill in the turbulent water.
One of New Zealand best road trips can be had along the coast at Kaikoura, not least for the changes post the 2016 earthquake (Wikipedia 2016_Kaikoura_earthquake) and the amazing road and rail reconstruction.
Looking back towards Kaikoura from the north - amazing sea colours not done justice here
Seals at southern end of Kaikoura - about a 20-30min walk. We made the mistake of doing it on one of the hottest days recorded in the area - 35 degrees C.
The walk to the seals
Crayfish done the "proper" way and a whitebait fritter sandwich - roadside grill southern end of Kaikoura , not cheap but better than that frozen stuff we get in Auckland - and the location - right on the beach !!!!