For rebevelling, a DMT D8XX or a belt-sander. For setting and polishing the edge, lapping film or wet/dry sandpaper over glass and/or waterstones. I often use a rubber and steel "stone holder" to hold the abrasives still and sometimes put the stone holder in a Panavise and tilt it at an angle (turns the abrasive in the stone holder into an infinitely adjustable Sharpmaker or freehand upsidedown EdgePro - I stole the idea from ksskss!).
If you're using an EdgePro to sharpen kitchen knives, please build a narrow elevated stand that lets you get the very heel of the knife to match up with the sharpening arm at exactly a 90 degree angle (this is not possible with the standard EdgePro system on all but a few Japanese-style kitchen knives where the edge doesn't start until almost an inch from the blade). If you don't, the EdgePro will eventually grind a curve into the heel of your kitchen knives which reduces their effectiveness on a cutting board (if you rebevel with the EdgePro, this will happen faster).
Taking that shortcoming into consideration and dealing with it, the EdgePro lets you concentrate on forming an edge and then going through all of the steps to remove the scratch patterns of the previous hones or polishing tapes without bleeding off your energy on cleaning up oopses (don't worry, you can still make mistakes with an EdgePro - the most common is pressing too hard - and you can slip and put nasty scratches in an otherwise pristine blade far away from its edge. Speaking of which, coat your blades in painter's tape above the edge to reduce such accidents from happening no matter which system you choose.) and focus on a sharp, strong, beautiful edge.
