Rubber Z3 floormats
The BMW rubber mats for the Z3 are Part # 82 55 9 405 043, and the locks to hold them down are 51 47 1 919 177.
I got mine (mats and locks) from z3solutions.com (plus you won't need the part number...).
Note that the driver's side rubber mat uses locks that are in the same place on the floor as the stock (carpet) mat, but the passenger side does NOT.
The passenger's rubber mat has lock holes that are farther back and closer together than the locks for the carpet mats. I expected the locks to match between carpet and rubber, and was a bit annoyed that they didn't, though I did go ahead and use them (and I like them). The locks for the rubber mats are more or less between the passenger's seat rails and out of the way (at least the way I installed them), and the rubber mats cover up the locks for the carpet mats, which is lumpy, but bearable...
You are warned by the installation instructions that if you take the locks out you'll be unable to replace them...