At HF most of the interference you're going to get from box to box is
either conducted along some wires connecting them or radiated by some
large metallic structure (the power cord, the house wiring, etc) that
is connected to wires coming out of the boxes and then picked up by the
antenna.

Although Roy has excellent points about what you need to do to get
solid EMI shielding, you can do a lot without plugging the holes in the
boxes.

Reg is right about the first step. Do you need extra measures at all?

The second step is plugging the BIG leaks, which would involve doing
things like filtering the unshielded cables coming in and out of things
(ferrites on the power cord, for example). Your boxes already have
some shielding by virtue of the fact that they're in metal enclosures
(I assume).

If you are having problems with, say, a switching PSU and you think
it's leaking in to the tuner, try this. Replace the antenna and
feedline with a good, shielded dummy load. Then see if there's any
change in the noise in your RX between setting the PSU on the tuner and
setting it elsewhere.

Dan