Start trek? Is that related to Star warts? :D
I wouldn't know. That never happened.
The other big gotcha with the question is that the EM spectrum is self-ignoring. You can cross 2 lasers and (in general) both will hit their targets with the same effects as if they didn't get crossed.
Right. Assuming your "shield" is em, and the incoming energy is em, the two waves pass through each other. Sure, they create an interference pattern, but that doesn't do you any good sitting behind the emitter that's doing the interfering as the wave wouldn't be modified once it passed the emitter generating the interference.
I guess a better solution would be to simply have a bay where Tribble's are provided with food and then they're dumped into space on the side that needs to absorb the impact of whatever weapon...
An old game called Traveller had "sand-casters" which had that effect for spaceships, except they used sand rather than the 90+% efficient Tribble replication engine....