I've always wanted to try out this theoretical real-time antialiasing trick with Amigas. You have the game set in EHB mode, all your BOBs and background graphics would use the first 32 colours, and all the BOBs have a EHB mask behind them which slightly overlaps the BOB its under (the pixel artist would determine the best mask). This would give the illusion of an outline around the characters which is semi-transparent and would help blur jagged edges, and could also be used for shadows below the characters. Or shadow character bad guys!
I'm not sure that'd actually work. The second 32 colours are always going to be the same as the first 32, just half as bright.
For antialiasing, you need to be able to blend foreground and background pixel colours together in a ratio proportional to how much of the pixel the foreground occupies using the blend equation below
pixelColour = fgAlpha*fgColour + (1.0-fgAlpha)*bgColour
where fgAlpha is the alpha channel value of the foreground for that pixel (in the scale 0-1, where 0 is completely transparent).
The alpha channel is where the antialiasing comes in. If you imagine a perfect 45 degree diagonal edge that you were antialiasing, it might cut a pixel perfectly in half and as such, the pixel at that point would have an alpha channel of 0.5.
What EHB ought to be good for, however, is realtime shadows.