Aw Una that's no fun! A trench coat does seem like a rather.. erhm, large.. item to misplace. I hope it turns up!
I have lost a stud from not one, but TWO pairs of gifted diamond earrings from my husband -_- The first was many years ago. I was performing and the earring got caught on my clothing and was torn out of my ear; I spent 2 hours after the concert looking for it but of course it was nowhere to be found.
The other was from this past April on our San Francisco motorcycle trip. On the FIRST DAY we stopped for lunch just a couple hours away from home, and while taking off my helmet one of the earrings was pulled loose and fell to the ground (which was covered in gravel, of course). Spent almost an hour looking for it, but eventually had to give up and continue along.
(Though I suppose these aren't as bad as this one: on our Yellowstone trip, one of our friends lost his wedding ring while on the road; his hand cramped up so he shook his hand vigorously and because he was wearing fingerless gloves, off flew the ring.)