Hiding sections of arbitrary models that lie one side of a plane

I'm looking for a way to hide a section of an arbitrary model in a free-standing portal effect (i.e. it's only visible one side of a flat object). I'll actually be revealing it from the ground up if that makes any difference.

Most of the solutions I've found use shaders, I don't know much about these but it doesn't seem like there's any easy way to combine them and I need this to work with an exiting collection of objects with lots of different shaders and materials already applied to them.

Can anyone suggest some alternate methods? I don't need the cut to be filled in, the plane covering it will be larger and opaque, I'm just after a way to hide a section of model that won't affect the way the visible section is rendered.