I believe all the processes of decaffination extract at least 99% of all caffine from the green bean (obviously some more than others). I'm sure that is far below any amount that your doctor would not want you to drink. However, you should consult your doctor on this. They would understand your situation and be able to paint a clearer picture of how much caffine consumption you are allowed. I'm also sure a doctor telling you to not intake coffee can tell you what foods are safe and which are not.
The Swiss Water Decaf website claims the following:
How much caffeine is removed in the decaffeination process?
"97% of the caffeine is removed. The trace amount of caffeine remaining should have no effect"
"Decaffeinated coffee is indeed without venom. It contains, at most, one fortieth of the amount of caffeine in untreated beans. Nor should the removal of caffeine alter the taste of coffee. Isolated, caffeine is a crystalline substance lacking aroma and possessing only the slightest bitter taste. Its flavor is lost in the heady perfumes of fresh coffee. So if you hear people say, "Coffee doesn't taste like coffee without the caffeine," they are wrong. The only real problem is how to take out the caffeine without ruining the rest of what does influence coffee flavor. But technology has triumphed, more or less. The best decaffeinated coffee, freshly roasted and ground and carefully brewed, can taste so nearly the equal of a similar untreated coffee that only a tasting involving direct comparison reveals the difference."