RFID tags inside metal items?
RF coupling
The &quot;perfect&quot; Faraday cage requires the metal to be a perfect conductor.  Copper is a great material for Faraday cages.
However, stainless steel isn't a great conductor.  It's ok, but you will find that some RF, particularly low frequency high power RF, will penetrate the case, and the RFID tag will affect that field.
However, you're probably not going to be able to use an off-the shelf RFID unit for this if you depend on RF coupling.
Magnetic coupling
Most inexpensive RFID tags operate on the magnetic field rather than the RF field, and fortunately for you many stainless steal alloys have very weak interaction with magnetic fields.
If you choose an RFID transponder with a large magnetic loop antenna, and you have the reader very near, you should be able to use RFID inside your stainless steel case with very few problems.
You'll want to experiment with different stainless steel alloys, and different transponders, but you should be able to find something off-the-shelf that works.  I'd aim for lower frequency RFID - I would expect 125kHz RFID to work fine in this situation.