Without details about the metal used, type/quality of stones, etc., I think you'll be hard-pressed to get anything concrete. Can you possibly take them to a jewelry appraiser in your area?
Sorry to hear that, though I don't know you'd need an ID to get an appraisal, except possibly if the item is left and later picked up, and the jeweler doesn't know you (as a repeat customer).
The pictures are really blurry, so the only thing I can make out is a "925" stamp which is silver, but they look to have a gold metal as well (whether it's real, plated, filled, I don't know). And I have no idea what kind of stones they are, though they look like peridot to me.
Perhaps peruse rubylane.com for similar styles to see if that yields a similar pair to get idea of what they are worth?
‘Green Amethyst’ is usually an alternative name for Praziolite, which is a bit hard to pronounce. That’s the name for green quartz (amethyst is purple quartz and is quite a bit more common). As mentioned above, it’s not of itself usually terribly expensive but certain designers sometimes charge quite a bit for their work. Mostly Praziolite pieces aren't expensive but they can be quite lovely.