RF Design: A Bluetooth Repeater
The passive antenna solution sounds attractive but, on the basis of reciprocity, if stuff could get out then stuff could get in and, that would negate the whole reason for a faraday cage? OK it's a bit more complex than that - I guess bluetooth and regular cellular transmissions are on different frequencies so you could filter in what you want passively and bidirectionally. 

I have a feeling though (without trying to do the math) that if you tried to formulate an answer based on what you "propose" and look at the link-loss of the rf you'd find it'll be almost impossible unless the handset and external receiver were bang-up close to the their respective duck antennas.

The 1st duck antenna will receive a tiny fraction of what the originating bluetooth transmitter transmits because it is transmitting power in all directions (I know it's not an isotropic antenna so don't shoot me!!) and all that power gets thinned out rapidly (1/radius^2). The receiving duck antenna has an effective aperture and that equates to a surface area - it dictates how much of the rf hitting it gets converted to power. At twice the distance away it will recieve a quarter of the power it previously did.

Now, say that power is received ok and fed down a cable some distance to a passive antenna (the duck outside the cage) - it will transmit that power in all directions (again don't shoot me on it not being isotropic) and the fraction that the final blutooth receiver receives is much, much smaller than if it were at say twice the distance of the first duck.

This leads me to conclude (without getting my calculator out and looking up the effective aperture of a duck at BT frequencies) that it'll only work if you get 1st duck up-close to the HS in the cage and the 2nd duck up-close to the receiver outside the cage.

EDIT - I used a spreadsheet and used antenna gains for a short dipole and yeah I know the formula below will be upset a bit in the near-field but I can't think how to calculate it any other way.



I've not mentioned the coax but it'll provide a really big loss if you haven't used the best you can get your hands on - try looking up coax specs on loss (dB/metre) at 2.45GHz.