kayork,
Jackie Kennedy's pearls and Barbara Bush's pearls were imitations made for them (by Kenneth Jay Lane.) There is a place for imitation pearls as fashion accessories, and these are special because they belonged to your grandmother.
As far as market value, what we generally suggest is doing a search on eBay of similar
sold items (items are only worth what people have demonstrated a willingness to pay for them.) Here, for example, are the results from a search for "Richelieu pearl necklace", sold items-- from highest price to lowest:
http://www.ebay.com/csc/i.html?_sop...+pearl+necklace&LH_Complete=1&LH_Sold=1&rt=nc
The prices realized are quite low for this brand. I say, just enjoy them.
Here is an interesting ad for Richelieu pearls being sold on eBay, with a box and necklace similar to yours:
http://www.ebay.com/itm/1946-RICHEL...746?pt=LH_DefaultDomain_0&hash=item58a07d46da
And still more ads-- I do like these vintage magazine ads:
http://www.ebay.com/sch/i.html?_odk...313.TR0.TRC0&_nkw=Richelieu+pearl+ad&_sacat=0
Hmmm, one of those ads calls them cultured pearls:
http://www.ebay.com/itm/1949-Richel...994?pt=LH_DefaultDomain_0&hash=item232afb3ab2
I wonder if they sold any real cultured pearls?
This ad shows different strands ranging from $2 to $35-- surely even then, one could not get real cultured pearls for $35?
http://www.ebay.com/itm/1950-Richel...485?pt=LH_DefaultDomain_0&hash=item439f5729b5
Furthermore, this ad (enlarged) contrasts Richelieu "cultured" pearls vs. "genuine" pearls-- sound like they were overly liberal with the use of the world "cultured":
http://c590298.r98.cf2.rackcdn.com/ESQ1_375.JPG.
I think you ought to try the test for nacre-- rub 2 of the pearls
gently against each other. If smooth, they are imitation. Real pearls would be a bit gritty if rubbed together.