In article ,
Joseph Gwinn wrote:

Wrap a piece of coarse-grit wet-dry sandpaper around a flat piece of
metal, and wet sand the surface flat by hand. Change sandpaper often.
If the mill has done its work well, it will not take very long before
all miil marks are gone. If desired, use finer grades of sandpaper to
eliminate the frosted surface. This can be carried to any extreme,
including mirror surfaces, which seems extreme for an anvil surface.
Unless you are a jeweler.

I don't know about that - my friend the armorer (plate, various sorts,
Italian 15th century being his favorite, as I recall) always kept the
anvil faces and hammer faces polished to a mirror shine. Not overly
difficult to maintain when in regular use. Takes a good deal of work to
get an abused rusty farm anvil up to that standard in the first place,
however.

Mine look like crap, comparatively, but that's mostly because they are
sitting around in one of the interminable phases of not getting much
work done while trying to get the shop ready to use. The older one did
get a full workover when I got it, and I oil them to slow the surface
rust while they wait for me to get things set up.

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Cats, coffee, chocolate...vices to live by