ungrounded chassis shielding
There is a big difference between mounting self-powered electronics inside an ungrounded conducting box and an ungrounded shield on a cable. Of course the electronics inside the box is protected but, if those electronics were fed from an external power source that is unprotected (i.e. not in the same "faraday cage") then you stand to make no gain.

So this is why you should ground the shield on a coax or twisted pair cable - an ungrounded shield only prevents differential voltages appearing on the signal cables. However, an ungrounded shield does not prevent common mode signals appearing on the signal wires - you must ground the shield to remove these.


  It is almost worse to have an ungrounded shield than to have no shield
  at all.


I have to disagree with this - the limited benfit of an ungrounded shield is that it applies the same interfering signal shape and amplitude to both signal conductors like this: -



And, providing you use a differential amplifier at the receive end, that interference is cancelled. You don't need to transmit a balanced signal from the send end but you do need to have equal wire impedances to ground at the send end and, by inference, you need equal impedance balance at the receive end.

The problem with the shield being ungrounded is the level of interference "given" to both balanced wires is much higher than in the case of a grounded shield and this means the receiver has to deal with a bigger common-mode noise signal and this is going to be harder to remove.


  Would it be safe to say that an ungrounded metal box
  provides good EM shielding granted that the electronics you are trying
  to protect are physically located at a sufficient distance away from
  the walls of the box?


No, not really - everything inside the box is protected - everything is being wobbled up and down together and each node-to-node voltage remains the same as if there were no interference - the problem comes when you make a connection to the circuit inside the box.