After you get your appraisal, now what?
Understanding appraisals will depend on what your objectives were in the first place.
If this was a new purchase, the seller probably made some representations at the time. Your appraiser may or may not have agreed with them. If you found important discrepancies in the description, these should be clearly spelled out in the description section of the report. If the appraiser thought that your diamond was misgraded, this will be clearly stated in the description. It may say something like XXX diamond accompanied by a report issued by XYZ lab identifying it as YYY with a copy of the lab report attached or it may just give the graders opinion. Your receipt from the seller will usually give their terms explaining what to do in this circumstance. Read them carefully and comply with every clause.
If you find the valuation is alarmingly low, read the description again. The appraiser may have missed an important detail, like the brand of the designer, manufacturer, or diamond, or they may have a critical error, like calling platinum white gold. Feel free to call them and discuss the matter. Also check the market being discussed. It may be different from the market where you bought the piece. If they are discussing the resale value used on the secondary market and you bought it new directly from the designers boutique, it is almost certain that they will find a lower value than what you paid.
The opposite is also true. If the valuation is especially high, make sure you understand why. It may, indeed, be that you got a fabulous bargain. It may also be that what they are describing is not an accurate depiction of what you bought. Most often, this comes up because the client made their purchase at a discount or internet seller and the appraiser chose local retail as the comparable market. This kind of change in market can be quite significant.