StaffSoapUI is great for testing web service calls. For web exception handling, another SmartBear tool - TestComplete - might be a better fit.
With SoapUI you can determine whether your REST or SOAP web service calls work as intended. So if your web exception is thrown at the time when a web page makes a call to a web service, SoapUI can help narrow down whether the issue itself is manifested in the web service. If not, it's likely in the integration of the call
AlumniHi Ismee,
As for TestComplete, here are descriptions of some product features that you might find useful for your task:
