Are you absolutely sure that the signal is being displayed as hi-def on your television? Even with interference, you shouldn't be getting a shimmering effect if you are using the component cables in a progressive scan mode.
Are you using the hi-def Xbox cables only out of the Xbox, or do you have two sets going to your TV (I can't remember if its even possible to have 2 vid outputs out of the Xbox anymore)?
Some tests to try:
1) Easiest is to pop in a 720p/1080i game if you have one... you should notice a visibly higher resolution picture. If you are still getting a shimmering effect while in 720p/1080i... well, I dunno - I've never heard of that before
2) If you don't have any high resolution games on hand, you can try switching the Xbox system menu to hi-def and see if you notice a difference.
a. Make sure you have the latest Xbox live system update. This can be obtained by either connecting to Xbox Live, or else having a fairly new Xbox.
b. Be sure that 480p is enabled in the video settings.
c. While holding down the L+R triggers, click both thumbsticks at the same time. You should see the video mode on your television switch over to 480p. Check your HDTV documentation to figure out how to check the current video setting on the TV itself.
3) What model Zenith are you using?