This was my grandmother's watch. I've been combing the internet and still can't figure out the model and year. I believe it's 1960s and originally had a black leather band (back of buckle picture says "PLAQUE G" and has a Swiss stamp and an AW stamp), later replaced by the speidel one shown.
It's super petite...about the size of my thumb nail. The hands and hour markers are slightly diamond shaped.
Help from the Omega watch whiz hive mind appreciated!

 

Typically, the Omega Sapphette series were in karat gold cases with finely faceted synthetic sapphire crystals. The crystal,in the subject watch appears (to me) to be an acrylic crystal because of the scratches. Please provide details as to how you are calling the subject watch as one from the Sapphette series. I have shown two Omegas ladie’s watches from the Sapphette series for comparison.

 

This is what happens when you have no clue! I've altered my post and added more photos. Thank you!

 

I think you have the age correct. Circa 1960 would be my guess. You don’t give enough information to determine if the case is gold filled, or karat gold. If it has a steel back, then my judgement says it is a gold filled case. If you might imagine this watch with a crystal with a plain edge (no facets), then check your on line references again, you might find a similar watch. In my view, this crystal is not original to the watch. It would originally have had a plain edged crystal.

 

The back is gold. I guess the crystal could have been changed out. Maybe that is part of making it difficult to find.