I'm working on running OutRun in a higher resolution using the native graphics (i.e. no new graphics are required).
In the below screenshot, I've split the image between the original resolution scaled up (left) and the higher resolution (not using scaling). Ignore the fact that the road and background are missing for now, as this is still work in progress.
This doesn't help objects really close to the camera, as the original sprite files aren't particularly high resolution to begin with. But it does help images in the distance. The Dreamcast port does something similar.
OutRun actually has five copies of each sprite, manually tweaked to look as good as possible at different zoom levels. I made an initial attempt to go one step further and completely replace the lower resolution sprites with their higher resolution counterparts. But the results didn't look good. I'll keep working on this.