Okay, I am completely unsure if I've EVER, EVER run into a shiney Pokemon in my Emerald but I have seen a shiny Pokemon and caught it on my Ruby.
Fffp, yes this is one of my long stories. FLUFFIN DEAL WITH IT
I was in Granite Cave and I had just finished talking to Steven in the cave. I was looking for any random items in the rocks in the chamber when there obviously weren't. I was getting ready to leave and i was right near the doorway when a wild zubat appeared. I was like, "Oh, jeez. Another one ag-ching-HOLY CRAP HVHJJFTYD"
A shiney zubat appeared! I swear my heart skipped at least two beats. I was freaking out and trying to be quiet too because everyone was in bed, lol. ANYWAYS, I immediately threw a Great Ball. It rocked 1 time, then the zubat popped right out. Ching, again. I slapped myself. Was this really happening? Was I having a dream? No. I brought out my Surskit, lvl 12, and used Bubble, which crashed down its HP to about a half an inch. I threw a Poke ball and it was caught.
Have you ever encountered a shiny on the gem games? Tell about it!