Do you know for sure it's emerald? It looks like it could be tourmaline or even dark fluorite. Could be emerald too, but I don't know if you know which stone it is for sure, since they were a gift?
That's what my uncle told me it is and I know he wouldn't lie to me since most of the jewelry I have is from him and he owns a jewelry store and he's had it for over 40 years that's all I can tell you wish I can tell you more