Well, since I'm a bassist, I don't use picks. How I get artificial harmonics is by picking the string w/ my index or middle finger against my thumb.

The real trick to this no matter how you go about it is to have a finger or the tip or your thumb just barely touch the string as you pick. Though using distortion will help these come out, I would practice it w/ no distortion so that you can focus on your technique more. Once you get comfortable on this you can do some exceptionally cool things (I know a guy who can get a phaser-esqu sound by doing artificial harmonics up and down the string).