I did a Google Search to answer this question. I am not aware of local people who appraise quilts, but you might be able to ask some antique dealers if they know someone skilled in this. My search found lostquilt.com/Appraisals.html and quiltappraiser.com as its first picks. I know that caring for them is equally important to have expert advice. Mary Ann Fugate, our retired Family and Consumer Economics educator, once advised me to soak old quilts in a bathtub. She recommended a gentle soap and no wringing of the quilt - just squeezing out excess water and rolling it in towels when done. She recommended Bovus, which is a shampoo that you can get at Farm and Fleet. It's something used to give a shine to animal coats for show at the Fair, but it also gives the same effect to old needlework and quilts. Lay the quilt flat to dry. Some people like to do that outside on a nice day on sheets.
You can find lots of tips for caring for old quilts by doing a search on Google.com about caring for old quilts or storing old quilts.