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.
Looking back towards Picton.