An appraisal will cost you some money, upwards of $150.00. If you think that your items are worth a great deal, go for it. But you may want to investigate for yourself in order to see if an appraisal is worth it.
Learn something about your cups and saucers first. Look at the bottoms of each piece to find the marks that can tell you who produced them. You can learn an approximate date of manufacture as well. Many companies changed their back stamps over time so this will help you get an idea.
Check your local library for books that can help you with the identification.
"Collectible Cups and Saucers : Identification and Value" by Jim Harron; "Kovel's New Dictionary of Marks" by Ralph Kovel; "Miller's Field Guide - Porcelain" by Judith Miller; "Pictorial Guide to Pottery and Porcelain Marks" by Chad Lage are just some of the books that may help you.
There are ways of locating items similar to your own online as well. Google image the backstamp, type of cup, color, pattern and see if cups and saucers like your own pop up. Beware of thinking that you have an expensive, high quality item by pattern alone. Copies of high end china are everywhere. Those copies can be nice when we don't want to use a very expensive antique piece of china for regular usage.
If you do think that your cups and saucers are very old or special, do not put them in the dishwasher. Clean them in warm water with a mild soap and hand dry with a soft cloth.