How to fix EMC problems for existing designs?
There are a couple of general strategies you can consider:


Add shielding if there isn't already.
Close gaps in the shielding. Remember the radiating efficiency of an opening in the shield depends roughly on the largest dimension (a 4" x 0.001" seam radiates nearly as efficiently as a 4" x 4" hole), so concentrate on breaking up the longest seams with gaskets or other types of conductive materials. 
Add EMI-absorbing material within the enclosure. This is usually a stop-gap to avoid changes in other parts of the design, but it's generally expensive and not necessarily very effective.


Beyond these general strategies, this kind of problem depends a lot on the details of your system and exactly what changes you can afford to make, so it's hard to be more specific about what you can do.