Please please please buy travel insurance - for so many reasons, it's a very bad idea not to do so. It's a terrible scenario, but one must consider it, as it does sometimes happen that traveling companions die whilst on holiday. And that's just one of many reasons to purchase travel insurance. There is a reason cruise ships have body bags and a morgue on board. You wont hear cruise ships shoulting about the deaths from the top of the roof tops - it's not great for marketing - but annually some 200 people die on cruise ships (about 0.001% of the total number of people cruising). Most deaths are from illnesses related to being old, with the majority being heart attacks.
All the costs pertaining to the death and transport of remains are for the cost of the family, who may or may not have travel insurance.
Also be aware that some port destinations require that the dead be disembarked, so you could well have to be transporting the body home from a "difficult" port. This also depends on the flag the ship is flying. It often happens that when somebody is ill the cruise ship evacuates them immediately from the ship to the nearest hospital.
Even under normal circumstances a death is very hard to handle, but if it happens whilst one's travelling it's even more stressful, and if one's travelling and has not travel insurance it's ultra stressful with large financial consequences.
To transport the remains back you'll need a funeral house where you are, as well as a funeral home to receive the remains back home.
Two parties who should be able to guide you with e.g. funeral homes to work with, and documents you'll need are:
Whilst they are likely to help guide you, note that these parties wont pay for anything.
Some of the exotic destinations cruise ships visit tend to work on "island time", which can be rather frustrating.
Even if you think you don't have travel insurance, it's worthwhile checking whether there was any "free" travel insurance offered with credit card purchases of travel tickets. It's also possible that your or the deceased's employer may automatically be supplying travel insurance.
Conversations about deaths on cruise ships inevitably get to talking about falling overboard. In fact, it's very difficult to unintentionally fall off a cruise ship; and people "falling" off are usually trying to commit suicide or are up to drunken shenanigans (overconsumption of alcohol is a huge problem on cruises - especially the party-themed cruises).