In trying to determine the identity of the namesake of the ship William Frothingham, I stumbled across the Winthrop Society. This society names a William Frothingham as an early settler of the Massachusetts Bay Commonwealth, but it is not clear if this settler has any connection to the William Frothingham after whom the ship was named. In any case, this society has identified a William Frothingham among the The Freemen of Massachusetts Bay 1630 - 1636.
Peter McCracken has listed William Frothingham in his Ship Index. He has also provided a research guide for maritime history on the Internet.
Vince Busam identifies William Frothingham on his page titled "Busam Immigrants to the United States, pre-1900". In it, he mentions a voyage made by the ship from Le Havre to New York on 12 Aug 1864. He got this information from Filby's "Germans to America" books.
If you're interested in any of the vessels that brought our ancestors across the oceans, be sure to check out TheShipsList Website at http://www.theshipslist.com/.
The Fine Art Emporium has a wealth of marine artwork that is worth a peek (nothing on the William Frothingham though). They are at http://www.fineartemporium.com/index.htm.
The Penobscot Marine Museum is located near the town of Belfast, Maine, USA. Their web site is at http://www.penobscotmarinemuseum.org/
The Heritage Centre of the University of New England, Armidale, NSW 2351, Australia maintains a website at https://www.une.edu.au/library/heritage-centre2