I agree with mdengraver, it is best not to polish after engraving if you don't have to.
polishing is part of the prep work. in some cases it may be needed like with inlays with excess that needs cut away and polished back, but in most cases it's preferable to do the inlays then polish back and then do the rest of the engraving so you don't have to polish over the engraving. you may also want to nock some sharp burs down that got missed during engraving, but some would argue that doing that is either a sign of lazy work or that it removes that "sharp hand cut feel" .. either way if you choose to polish after engraving I would advise you to keep it to a minimum and stick to the highest grit paper that you can to achieve the look and feel that you want. remember, all those fine shading lines are just a few careless sandpaper strokes away from being polished off..
I sometimes run a few passes of 1500 or 2000 grit paper over a knife part or bolster (usually 416 stainless) after cutting all the outlines and borders, just to take care of any burs I might have missed and give it a smoother feel in the hand (since knives are cutting tools and meant to be handled). But I'd never use anything coarser than that, and never after shading. And by a few passes I mean like 2 or 3 tops.
That said, I agree with the above--on jewelry all the polishing should be done beforehand.
Most of my engraving is on jewellery. What I do is get them to finish the piece completely, then engrave it, and drop it back to the polisher for a very very light rouge with a mop that's specifically used for that. If they're going hard enough to round the sharp edges noticeably then they're going too hard. It removes any tiny scuffs and, without the final pass, the engraving can almost feel rough(?) against skin, particularly the wrist.
When I started working for my self a few years ago, jewelers kept giving me rings and stuff at 400 grit finish and then obliterate the engraving while polishing it up. Since starting at my current job I put my foot down and won't engrave something unless it's either fully finished or a light rouge away.
Note: most of my work is lettering and dates. I rouge the decorative pattern stuff myself
Thanks for the information I mainly wanna do stone setting with the engraving. So I saw stone setters marking out with their dividers (on a fishtail setting for example) and then using the graver. Do you have to use sanding paper and do a normal polish afterwards ?
Normally when setting we would have them pre-polished to just before the rouge finish (cant remember the name of the green wax) and then set it. Other's might do it differently, but to keep things clean and sharp looking you want to have do as little work as possible to it afterwards.
One thing to keep in mind in mind is that working on a ring with a sanded finish makes it much much easier to show the layout lines and cutting angles on video, the people doing the demos might do it differently when actually setting jewellery and are working on brushed/sanded metal to facilitate showing how they go about doing it.
Personally the order of operations I use for rings and the like are: manufacturing, pre-polish, setting, rouge polish, engraving, very very light final rogue polish.
I probably sand more than most of my fellow engravers after engraving. I slip lots too still, or break tips off carbide gravers and have to do repairs. Hard backing reduces unwanted effects but something like a firm rubber backing helps get a smooth finish. But you're talking about a ring? Could we see any pictures? Surface prep first is always a must but I'm not sure I've ever done a piece and not sanded at some point. I try not to with bulino though, you lose hours of work in seconds.