Put in four dice, and secure with 3 rubber bands. Shake and go. This was actually created to help generate "analog entropy" for cryptographic key generation, but there's no reason it couldn't be used for board games, etc.

Shake this instead of rolling four dice on a table. It makes sure that there is no ambiguity about the order of the four dice. Put in four D10s and each shake generates a perfectly uniform number between 0 (0000) and 9999.