iPad Sim Card Stuck in Slot without Tray
Yes, I was dumb enough. I thought it was a slide down door. Tray popped out and I didn't see it fly by.
Quite a few people said you're out of luck. Apple won't even touch it. One poster said he heated up the tip of a very small safety pin then poked it into the plastic and held it for a minute to kinda solder it on. Other said they tried very small tweezers.
I solved this issue myself by doing something a little different. (Do this at your own risk! I'm not going to be held responsible.)
The SIM card and the SIM are both the same thickness, so I didn't have to worry about sticking anything too wide, or large, into the slot.
First thing I did was cut the short end of the SIM card, (not the SIM itself) about 1/4 inch (6~7mm) wide. and round the corners of one end.
I then used "Loctite" Super Glue GEL CONTROL. Use the gel because it won't run down the card.
You only want to touch the edge of the card with the glue bottle dispenser tip. Don't make it any wider than the card.
I then CAREFULLY inserted this end of the tool with the glue on it into the SIM slot and touch the edge of the SIM itself with your new "glue-on-a-stick" and hold it there without moving it for about 10 seconds.
I slowly removed the card tool I made, and low and behold the SIM came out with it.
I'm not recommending you try this, and I won't be liable if you ruin your iPad attempting it. BUT from all of the comments about selling it on eBay or taking it in to Apple and having to buy a replacement at half off, unless you purchased the Apple Care, "this isn't a manufacturer's defect, it's an "I screwed it up" defect so your mileage may vary.
Hope this helps somebody.
iPad Air