The answer is both “a lot” and “not much”. The reason is that no two diamonds are alike and no two certificates (or more properly stated “reports” are alike). What you do get from a diamond report is a grading that was made independantly of your jeweler. Though also subjective, it’s bias is to it’s own laboratory not to the person selling the stone. That means that your jeweler should also examine the stone and give an opinion. Without your expert looking at the diamond your are limited to one opinion and a lack of explanation. What you do get is that with experience you have a good idea of what to expect. It really narrows the number of stones you have to look at to find the right one that meets expectations and value.
The report can fool you a bit as well. Many years ago the diamond was supposed to be looked at through the pavillion of the stone for more accurate color grade and then again from the top for an incidental color grade. That practice is gone and seemingly replaced by ever finer cut grading systems. But light only bends to one angle and the incidental light is not entirely eliminated even in a stone that is cut to exactly the proper angles for brilliance and fire. That incidental light can make a high color grade diamond look yellower than a lower color grade diamond. This is known by cutters and many jewelers but the pressure to just use “paper” (the grading report) is strong in the industry. So much so that it’s entirely ignored in pricing and never even mentioned by a dealer or cutter except in certain fancy cut stones such as pearshapes.
A clarity grade does not evaluate the inclusions for their type, only for their grade as determined by that laboratory. Some labs do say what the inclusions are but is a crystal better than a feather better than a cloud? Is the location important? In diamonds of a higher than average clarity grade you need to discuss the inclusions because the report does not explain their effects. A cloud in the culet can make the whole stone look softer or even hazy. A knot or crystal on the surface can be knocked out. When I’m buying I negotiate on dozens of issues that are or are not touched on in the report but can affect beauty or durability. No two diamonds are alike so the cutting and grading are not exactly identical. You should see diamonds side by side to decide. Buying a diamond is too important and too sentimental to decide by looking at “paper”.
How well a diamond is cut is the most important aspect of a diamond as far as it’s beauty goes. It’s also important for durability. A diamond cut off-grain is easier to chip than a diamond with the grain oriented horizontally. Light only bends to one angle so even slight variations have an impact. Grades all have ranges and it takes an expert to explain why one stone seemingly the same as another on paper is better. In some cases it will just take looking at them side by side. Sometimes it’s obvious. In general use an expert for this important decision. It’s more than worth it and we’re here for you.
