At a glance, those seem really nice.
Before the experts here would give you advice, they'd probably need a bit more to see. Perhaps some zoomed macro shots on white background in daylight would be a good start. Don't be shy to post lots of images of the pearls, pendant, findings and clasps. Are there any hallmarks on the clasps. or trademarks on the boxes?
Likewise, could you post the picture of your grandmother? Do you know how she came by them?
If indeed, these are from the 20's, it is possible they are natural and could retain significant value.