I’m surprised that Amalfi has no naval museum, nothing to remind us that Amalfi was one of the four maritime republics of medieval Italy. That fact is recalled by the presence of the Amalfi coat of arms on the modern flag of the Italian navy—along with the other three: Pisa, Venice, and Genoa (all of which have naval museums, I bet—but don’t know). That is a quiz show question, by the way: Name the four maritime republics of medieval Italy. Almost no one remembers Amalfi.
OK, I checked. Genoa has TWO!; Venice, one; Palermo has turned the old Bourbon shipyards into a naval museum; Trieste has one; Nardò, near Taranto, has one; Bologne has one, as does La Spezia, Imperia, and Caravaggio (not the painter, dummy, the town. See 45° 30' N, 9° 38' E). Pisa? I’m not sure, but at least they have that tower thing. But Amalfi? The place where the first Maritime Code, the so-called tavole amalfitane, was formulated, a code that regulated maritime trade in the Mediterranean for 500 years? The place where Flavio Gioia invented the modern compass? They have a Farming Museum and a Paper Museum. Go figure.

In Naples, they could have turned the old and historic Arsenale—the naval shipyards— into one, but they didn’t. That part of the port definitively disappeared during the great rebuilding of Naples—the risanamento —in 1900. So if you want naval museums in and around Naples, here’s what you’ve got:

Museum of the Sea—Bagnoli
Founded in 1992 as part of the Nautical Technical Institute “Duca di Abruzzi”. The museum hosts a collection of models, nautical instruments, and a library.

Museum of the Sea—Ischia
Founded in 1996, the museum is housed in the 17th-century Palazzo dell’Orologio in the historic center of the town of Ischia Porto on the island of Ischia. The displays occupy seven rooms on three floors. There are exhibits of nautical instruments, naval uniforms, model ships, a philatelic exhibit of stamps dedicated to the sea, and a photographic exhibit dedicated to both the maritime navy and commercial fishing fleet. Given the Greek and Roman history of the area, the museum houses, as well, a display of maritime archaeology.

Museum of the Sea—Procida
This facility is mostly a historical library dedicated to the commercial fishing fleet on the island, a traditional occupation of the people of the island. As well, there is a section dedicated to maritime religious rituals.

National Museum of San Martino
In Naples, the "Sezione navale” is an adjunct of the National Museum and is housed in that facility on the San Martino hill, adjacent to the Sant’Elmo fortress. The basis of the museum was a donation of the entire collection of the shipyards at Castellamare at the end of the 1800s. An extensive display of models of the many ships built and launched at Castellamre over the years, both sailing and steam vessels. The museum is currently undergoing restoration.

(image, above: from the museum in Bagnoli)