I recently acquired a lot of old imperial guard. They're mounted on the old square bases which I don't really like the look of. I know I've heard of people migrating old minis onto the new bases, but I'm curious how to get them off without damaging them.

Any tips?

I clip around the figure's round base with small pointed clippers ... then sand & file off the excess ... I've done it ...  

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Legion 4 "Cry Havoc, and let slip the Dogs of War !" ... "People sleep peaceably in their beds at night only because rough men stand ready to do violence on their behalf."

Use a sprue cutter to make cuts at a diagonal across the Epic base that don't line up across any of the individual mini bases.  Reason being, if you cut across the Epic base carelessly you can create a break that continues right on through the mini you are trying to extract.  You should get a bunch of tidy triangular sections with intact minis on top once you're done.

After that, it is just a matter of going around each mini base with a sprue cutter and clipping off the excess.  The round portion of Epic base left on the bottom can then be removed either with a razor or the sprue cutter.

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WAAARGH!!
The Lost & the Dipped

Awesome. Thanks!

It also depends on the glue that was used to attach them to the base. If it was super glue, a stripper that is safe for plastic (Simple Green is the popular choice here) may dissolve the super glue. It may not loosen the figure all the way, but enough that you can either gently lift it out of the hole in the base or flex the base to crack the remaining seal. I have had success with this before. If it was plastic cement, however, you are not so lucky and will need to follow the above suggestions. I have done both before; if you have to cut the bases, I hope you don't have too many to do!

With some troops it's also possible just to use a VERY sharp razor and slice them off neatly at the feet before reattaching them with plastic cement to a flat surface.
The only down side to this is that you must be careful not to snap the models legs.

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Or leaving the remnants of the base and leveling off with a deep layer of flock/talus.

On another note, if you get a stand of the metal Epic minis you can just dunk them in acetone.  It will turn all the CA into rubbery goo and you'll be able to easily pull the minis free.

Plastics & some resins are soluable in acetone, so I would not try this with the older Epic minis & FW stuff.

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WAAARGH!!
The Lost & the Dipped

I've been using the snip-and-knife method and so far it's worked wonders. I got the better part of an infantry company done in an hour or so last night.

I messed up with a couple of rough riders because they were on the newer, softer slotta bases which didn't cut as well. It's nothing that made them unuseable, plus I have a ton more than I could feasibly use.