If you don't get anyone who recommends a place specifically, I would google antique appraisers, raleigh, nc. A lot come up, then just start calling a few, and see who specializes in silver, as not all antiques are the same. and go to the one you felt most comfortable with.
You can also get a silver marks book, (any big book store should have them) and you can go through your own silver, looking at the marks, and the designs, got an idea of dates, and makers, and an idea of what they are worth. It'll also teach you (in most cases) how to tell if it IS silver or not. So, I would suggest that prior to getting anything appraised, and that's educational and fun.