Another way to do this is to use the typeof operator.
In JS if a variable has been declared but not set a value, such as:
var x;
Then x is set to undefined so you can check for it easily by:
if(x) //x is defined
if(!x) //x is undefined
However if you try to do if(x) on a variable that hasn't even been declared, you'll get the error you allude to in your post, "ReferenceError: x is not defined".
In this case we need to use typeof - MSDN Docs - to check.
So in your case something like:
if(typeof jsonObject !== "undefined") {
    //jsonObject is set
    if(jsonObject.errorMessage) {
        //jsonObject set, errorMessage also set
    } else {
        //jsonObject set, no errorMessage!
    }
} else {
    //jsonObject didn't get set
}
This works because if you have a variable set to an empty object, x={}, and try to get at a variable within that object that doesn't exist, eg x.y, you get undefined returned, you don't get a ReferenceError.
Be aware that the typeof operator returns a string denoting the variable type, not the type itself. So it would return "undefined" not undefined.
Also, this very similar question on SO that could help you: How to check a not-defined variable in JavaScript
Hope this helps.
Jack.