SINGAPORE—When MS Selandia made her maiden voyage from Copenhagen to Bangkok in February 1912 she transformed the ocean-shipping industry, launching an era that would see the shift to oil from coal as the dominant fuel for ships.

Now, 100 years later, a few shipping companies are moving toward a new fuel source, deep-chilled liquefied natural gas, driven by tougher environmental standards, higher oil prices and greater availability of natural gas. Many in the industry see LNG as the ship fuel of the future, given seemingly...