A cooling method is provided which includes providing a cooling apparatus that includes one or more coolant-cooled structures attached to one or more electronic components, one or more coolant conduits, and one or more coolant manifolds. The coolant-cooled structure(s) includes one or more coolant-carrying channels, and the coolant manifolds includes one or more rotatable manifold sections. One coolant conduit couples in fluid communication a respective rotatable manifold section and the coolant-carrying channel(s) of a respective coolant-cooled structure. The respective rotatable manifold section is rotatable relative to another portion of the coolant manifold to facilitate detaching of the coolant-cooled structure from its associated electronic component while maintaining the coolant-cooled structure in fluid communication with the respective rotatable manifold section through the one coolant conduit, which in one embodiment, is a substantially rigid coolant conduit.