Not infrequently, someone will show me Grandma's treasured pearls only to have me point out that they are simulated pearls. If Grandma was a depression era bride it's particularly likely. Pearls were not cultured until the early 1900s and not customarily given as gifts to sweet sixteens and brides until the 1930s. Prior to the introduction of cultured pearls, natural pearls were the only ones available and they were rare and expensive. Pearl prices have gradually become more affordable over the decades as more become available and more countries become involved in pearl culturing with both seawater and freshwater pearls.
There are many do-it-yourself tests for discovering if your pearls are real. I'm giving you three of the easiest and most accurate that you can do at home.
Usually by combining these three methods you can determine if your pearls are simulated or real. Grandma may have never been sure, but you can probably figure it out. And if Grandma's pearls survived this long, real or fake, they may be worth re-stringing or you may wish to re-design them entirely with the addition of modern beads or clasp.
Natural Pearl: a pearl that is found growing naturally instead of farmed
Cultured Pearl: a farmed pearl
Simulated Pearl: a manufactured pearl--not a pearl that is grown