Can you just transform the scope subsequent to the callcc into a delegate, store it in your Continuation object, and then execute the delegate when it's called? Yes, you need compiler support (since you need to transform callcc() from a keyword or method call into the beginning of a new delegate and you need to find the ending spot of that delegate appropriately). And anonymous delegates aren't a part of the CLR, but there's a sample implementation in "The C# Programming Language."
I bet I'm missing some obvious semantic issue.