Not all graders of stones are equal, nor is the value of their cert. I know of a few places here in the States that will only accept a GIA cert. Warning: Spoiler! (Click to show)
My Wife's engagement ring came with a GIA cert, but I do not believe the cert number is inscribed on its girdle. However, I've seen the stone under a microscope while its loose and you can easily see it matches the plot that is on the cert (showing where any inclusions are and the type of inclusions). In addition to color and clarity, GIA certs also reference the carat weight, cut (mentioning extra facets if any, girdle thicknes), floresence, they have a map plotting out the stone, and a few other things I'm probably forgetting at the moment.
While a GIA cert does not create the premium that one would get for buying a stone through Van Cleef, Cartier, or Tiffany, once you are buying something that's 1.5 carats or more I would only purchase something that has a GIA cert. Not specifically for any kind of premium, but as proof that what you are buying is in fact the quality that you are paying for. Having an independent appraisal from a respected company gives some piece of mind that some place (even if its good quality jewelry store or boutique) isn't calling a stone an F when its a G and saying its a VS2 when its maybe an SI1 in an effort to sell the stone at a greater price.
yes. with GIA you can be sure you have the strictest grade possible, and that if you ever go to re-sell, you wont be told that the stone is of a lesser quality than you were originally. told.