Scratch marks are impossible to remove, so prevention becomes important. Always place a rubber mat in stainless steel sinks.
To remove burned on food from the surface of a stainless steel stove, boil some water (wear gloves) and pour directly onto the spill. Let it set a few minutes. That helps loosen the food making removal easier. In microwaves, wipe them down with boiling water then scrub with Cameo. Cover your food to prevent the splatters.