Editing 1st Marine Expeditionary Force (section)

===Shields===
In general, transporters could not be used while the deflector shield of a ship was active, or a deflector shield was in place over the destination.  However, it was possible to take advantage of EM "windows" that were created by the normal rotation of shield frequencies.  During these periods, a hole opened through which a transporter beam could pass. To use this window, timing needed to be absolute and usually required substantial computer assistance. This technique was theorized and first practiced in 2367 by USS Enterprise-D transporter chief Miles O'Brien. (TNG|The Wounded)

Magnetic shields could also be used to prevent beaming. Rura Penthe was protected by such a shield to prevent prisoners from escaping. (Star Trek VI: The Undiscovered Country)

There was a type of shielding that allowed transport, although it had the limitation of not allowing phasers to be fired through it. (TOS|The Return of the Archons)

The limitation of transporters versus shields was not universal, however.  The Aldeans were able to pass through their own shielding using transporters, though the shielding was impenetrable to other forms of technology and weapons. Similarly, both the Borg and Dominion used transporter technology that was able to penetrate standard Federation shielding.  Some adaptations, including rotating shield frequencies, could inhibit this ability but not eliminate it altogether.  (TNG|Q Who; DS9|The Jem'Hadar)