How to polish phone-screen and watch scratches

Phone screen glass should be polished with diamond paste,  phone screen protective film may be polished with baby powder. Don't confuse what you need to polish :) 

Keep in mind that phone screens may be coated with  anti-reflection coatings, and when you apply the diamond polishing paste, you not only get rid of the scratch but also polish off the coating. So, a glossy spot may appear where the scratch was. If you want this spot to disappear, you will need to polish the whole screen, so the whole coating will be polished off too. Scratch may be too deep to polish it off completely, so you may just to try to look it less annoying.  

Most scratches from glass or sapphire can be easily removed with a bit of diamond polishing paste and a soft buffing cloth. The major point is to select right grain size and appropriate grain size set.   

Grain size selection depends on scratch depth, but in most cases you may use the following set, taking next grit size, when scratch looks smaller:
-  5/3μ = 4000 = M4  - soften the edges of the scratch and reduce it;
-  3/2μ = 6000 = M1.5 - intermediary polishing;
-  1/0μ = 15000  - remove the scratch;
-  0.5/0μ = 30000  - final/mirror polish.  

Diamond paste concentrations to use:
- normal - occasional, home use;
- high - professional, phone screen polishing;
- extra high - professional, watch glass polishing.