After decades towering over the river, the last of the structures is being dismantled this week, girder by rusty girder.
One is to survive, however, to produce "virtual" vessels.
The cab from one of the cranes has been shipped to the Scottish Maritime Museum at Irvine on the Firth of Clyde.
Curators hope to turn it in to a new ride, a kind of cockpit simulator of the kind used to train airline pilots.
Museum director David Mann said: "We have very loose plans to turn it in to some kind of an interactive exhibition.
"This would be something that would enable people to feel what it would be like to work up on one of the crane cabs.
"Our volunteer engineers are already thinking about how this might work.
"We would want to do as little to the cab as possible so that the experience was as authentic as it can be."
The museum can't save a whole structure - Mr Mann stressed they wouldn't have the resources to maintain it.
It has also still to identify any funding to turn the cab, currently in storage, in to the attraction it would like it to become.
The decision to remove the cranes sparked concerns about the long-term future of Govan.
It is understood the fixed cranes, despite being put up in 1974, remained serviceable before being dismantled, and had been approved by external inspectors, despite an incident when a jib fell off one some years ago.
Yard owner BAE Systems said it preferred to use mobile cranes, which it sees as more flexible, and which are shared between Govan and its second Clyde yard, at Scotstoun.
The company is currently preparing to build a whole new generation of frigates for the Royal Navy, Type 26 Global Combat Ships. Its preferred option is to do so at a single site, Scotstoun. That would mean Govan shutting by 2017, at least as a naval shipyard, with its remaining workers transferred north of the river. Some industry insiders believe the fixed cranes could have helped secure new jobs in civilian shipbuilding at Govan. Others disagree.
The yard - still referred to by many as its historic name of Fairfields - has lost cranes before. Its giant Titan crane, put up in 1911, was taken down in 2007 to make space to build giant chunks of aircraft carriers.
Parts of the latest cranes to be dismantled are going to the Fairfield Heritage Centre at the yard. The rest, apart from the cab going to Irvine, will be sold for scrap by yard owners Clydeport.
Mr Mann, meanwhile, said his job was to save the heritage of the yard, even if, he conceded, the cranes are "not particularly old".
The museum already has a great deal of what used to be Govan's industrial heritage, including the 1872 glass-roofed Linthouse engine shop, moved brick by brick from the Clyde.
"We're not moving the whole of Govan here," Mr Mann stressed. "But we have very strong links with the yard."