My wife and I recently returned to NZ from a cruise in Japan which included a port in Jeju Island (South Korea). We used 2 Degrees roaming quite a few times (roughly 8 days)when we were off the ship in port and travelling around. You certainly can't beat $8 a day and our connection was reliable. In Japan the partner was NTT Docomo and not quite sure who it was in South Korea. 

In the past we would have normally gone with a local sim card but we worked out it wasnt worth that investment. 

We had Starlink on the Celebrity Millenium. Most ships have this availabilty as a premium-added value