Emerald
Emerald can be caught by Fishing in Stage 1 and Stage 2.
Stage 1[]
The Emerald can be acquired by Fishing with a Tough Fish Pole (or better).
It has no use before reaching City Island. Post-game it can be sold at Antique Shop for 15 dollars to help you afford other things.
Stage 2[]
The Ruby is a 4 star tier item obtained through Fishing in the ocean with Universal Fish Pole with Good Bait (or better).
It has no use before the End Game Quest. Post-game it can be sold for 1500 dollars at Jewelry and Designer Goods Store on City Island.