For my own, I tend to be very analytical (OK, I really mean anal... ), so if the piece is to be warm or cool or filled with contrasts I like to know what color combos I need to get me there. Some colors help to mute others, while other colors serve to do the opposite.
I don't often trust that what I see is exactly what I need to reproduce or not. My television has its settings, from the factory, that may show its images with higher contrasts. Some types of paper can make a photo or printed image either more saturated or muted. Even different printers with their proprietary inks can be different. Most of the color differences may be very subtle, but the eye can still see that there's something not quite right. So, my own answer lies in the use of sampling/color profiles to help my untrusting eye/brain somewhat trained. However, I do like to hear of what process others use, as I'm never too old or too pro to learn more.