You can get shielded ribbon cable, though it costs the earth. Sticking a solid chunk of metal under the board can help, though making the board four layer and devotog the two inner planes to solid 0V and +5V planes works a lot better.
Clamping a ferrite core around your ribbon cable might help - if you've got enough ribbon cable and a big enough ferrite toriod, it can be even better to wrap the ribbon around the torrod once or twice to make balun.
The real trick is to work out where the spikes are getting into your circuit, and how the current spikes get to traverse your board - if it is the current spikes that are the problem, as if often the case. Once you've found a path, blocking it is often relatively easy.
---------- Bill Sloman, Nijmegen