I don't know if this is an appropriate question but I think historians would know the answer. When museums are loaning priceless historical objects like the Magna Carta for example, to other museums overseas, do they fly it over, or ship it over? I realize this might seem like a dumb question but wouldn't it usually be safer transporting it by ship?
Well, it could be a number of ways depending on the object. If I'm loaning some objects in the same town, and they'll fit in my work vehicle, I'll wrap it up and bring it myself.
For major shipments across longer distances, I generally see museum contract with fine art shippers, who are professionally trained to deal with art and fragile historical objects. They cost an arm and occasionally a leg too, but I'm certainly not trusting a Diego Rivera or a Federal style dropleaf table to FedEx.
Now as for the overseas portion of your question. Most museums that need to transport objects overseas, or are requesting objects from overseas are larger, and can afford to do this. Many of them send one of their collections team along with the object to courier the object from start to finish.
Basically it goes like this:
Object is in the starting museum.
Collections staff complete a condition report, then wrap and pack the object.
Depending on the object(s) the courier could go alone or with another member of museum staff, or with a team of security guards to the airport (I'll touch on why air in a minute).
Courier drives the object into the airport where they watch it get loaded on the plane (I've never done this myself so I'm not certain of the exact procedure here, but this is what several museum couriers have told me).
The courier then boards the plane.
Plane arrives at destination, courier watches the shipment get removed from the plane, and delivers it to the receiving museum where another condition report on the object is completed.
If the courier is smart, they then use several vacation days to enjoy a nice trip abroad, since their plane flight has been covered.
The idea is that the courier keeps as much physical control of the artifact as possible.
Now why a plane? Usually it is faster, cheaper, safer for the artifact, and a lot easier to keep a courier with it. When I say safer for the artifact, I would much rather have my artifacts reacting to a change in air pressure and temperature that accompanies a flight than the prolonged exposure to the salty air and humidity that would accompany a trip on a ship.
I should also mention that this entire trip has been paid for and insured almost always by the borrowing institution. I hope that answered your question.
You might try /r/MuseumPros!