AndrewC: Usually it can be done via the video cards control panel/driver. Just look for scaling options (I know that both Ati and nVidia support this).
Thanks! In my case, it's Intel graphics on a netbook, so there's neither ATI nor nVidia options.
BUT! Advanced, then go to the Intel stuff tab, then there's a pop-up application, and somewhere around there there's a button of "scaling options". Which includes "preserve aspect ratio" (scale up by the same amount both ways) and "center desktop" (don't scale up). So now I have HOMM3 running a bit small but perfectly clear in the middle of a screen. Woo! Thanks!