If you are comfortable with French language there's a site describing such
repetitive failures otherwise Babelfish is your friend !

http://www.z3club.fr/modules.php?name=Forums&file=viewtopic&t=9593&postdays=
0&postorder=asc&start=0.
In this thread you'll see the pics of my gauge.

http://www.z3club.fr/modules.php?name=Forums&file=viewtopic&t=1272&highlight
=jauge
This thread contains the fuel pump dismanteling procedure and several
descriptions of different failures, including one that is very similar to
yours.

My problem ended with the fuel pump replacement.
I did begin the job, making the proper tool (that I described on the site
above) to dismount the big pump's nut. I found the ceramic substrate, where
the thick film resistors are deposited, broken into several parts, some of
them remaining in the tank.
Looking under the car, I noticed that the two rubber bands placed between
the thank and the clamps were almost completely out of their normal
position. Afraid of what might have been at the origin, I asked BMW to check
a possible thank distortion, the venting hole and the fuel distribution
checking the pressure at different places. Fortunately for me (and my
wallet), the fuel pump only (including the gauge) had to be replaced. They
had also to reprogram the OBC giving DTE errors.
Since I initiated the repair, I didn't place any claim at BMW France !

In the second post above, you'll read the history of a guy owning a Z3,
don't remember if it was a coupé or a roadster, who is at his second thank
replacement. The gauges keep breaking driving him nuts.

In addition, search for "venting hole" in this group, Nov. 2007. I got some
interesting clues from Jeff Strickland and Fred W.

The gauge issue is an old and common problem on the bimmers.
I classified them under several categories :
* The fuel, especially if containing sulphur, may corrode the tracks of the
gauge. In this case a dismounting and a cleaning solves the issue. Then the
gas needs to be selected as sulphur free. Some people put an additive in the
thank. In my opinion, this might be harmful wrt other parts of the engine if
not homologated by BMW.
* The gauge, when the thank is completely full, may touch the upper wall of
the thank, especially if you don't take care of those f.cking speed bumps
they put almost every where, shocks might result. I also think that
cornering might, in some conditions, provoke shocks of the gauge against the
tank. The result of these shocks may either be a ceramic displacement or a
damage. Removing the pump is easy. The repair as well. Some pictures
illustrate the gauge dismounting on the site above.
* The thank, for some reason already discussed in this group, may be under
severe depression causing the walls to get closer, possibly jamming the fuel
gauge and further on its damage.
* erratic and random readouts. I didn't manage to correlate them to any
reason. I had issues at 500000 km (now it has 102000 on it). Whilst the fuel
level was correctly indicated, the Distance to End was unconsistent and
varying for several fillings. Once I even couldn't start the engine. Opening
the thank cap and opening and closing the hood solved the problem? Either an
overpressure (due to the sun in summer) or a stuck relay released bu the
shock of the hood.

About the parts and the drawings, you may have access to the ETK/EPC on
line. Have a look on these sites:
http://bmwfans.info/original/E85/ or
http://www.realoem.com/bmw/select.do?vin=&kind=P&series=E85&arch=0

Also worth to buy the TIS on ebay. Associated to the ETK, it's less than 10
Euros. TIS help to troubleshoot the failures. However don't expect a miracle
!

Feel free to ask more if needed.
Good luck

BTW, what model of Z4 do you have ?
May you describe a little bit more what your problem is and what did the
dealer diagnosed ?