Don't know about Windows but on Linux I spawn an X session with a virtual framebuffer and arbitrary resolution, spawn a browser there pointed at URL and make a screenshot.
Was going to suggest this. Make it take up more space on your screen, that's more pixels in the same pic. You might need to do that anyway, if you're on an unusually low (nowadays) resolution: Otherwise the whole pic will be too small to make stuff out on high-res screens.
