When searching for information about a topic such as art, you need to be specific in your search terms. Use details such as the type of portrait. Is it an oil painting, a watercolor, photograph, or pastel?
Learn as much as you can about each portrait. Knowing the name of the artist or subject can be a help. Where did you get the portraits? Did they come from family? If so, pump family members for information. Check the back of each portrait for labels or auction house marks. If there is a gallery label, that means that at one time someone thought the portrait was of some value. Contact the gallery, if it is still in business. Framers can also be a source of information if you see a framer's tag.
Look for a signature. Google the artist's name to see if you can find information online. You can also look up the artist's signature on one of John Castagio's several artist signature dictionaries. The site Artnet or askArt may help you with that as well. But not all art is signed. A prolific artist may not have signed a work if it was not intended for sale or if the artist died before signing it.
Check with an auction house that specializes in art or antiques. They will offer some information or an estimate if they feel the work is of any value.
A book may help you learn more about finding value in art. Try "Art Dealer's Field Guide - How to Profit in Art, Buying and Selling Valuable Paintings" by Ron Davis.
Check out some of the online appraisal sites. They are inexpensive but may help you a bit.
Take the portraits to an antique or art dealer (email first with good photos) to see if they are interested. You don't have to commit to a sale but may find some useful information.
If you think the portraits are valuable, you should have them appraised by a professional. Find a qualified local appraiser who specializes in art or antiques by searching online for the American Society of Appraisers or the Appraiser's Association of America.
Finally, decide what you mean by valuable. Are you thinking of value in the thousands, hundreds of thousands, or a couple of hundred dollars? Old portraits are popular in today's decorating. Just pick up any interior design or popular home decor magazine and you will see older portraits on the walls. You may be able to sell them even if they are not worth very much especially if there is a charm factor. If the portraits will not earn you what you would like you can always hang them in your own home.