I see your point, Lasse. Thanks again for the explanation.

By testing for the specific exception, (e.g. a NullPointerException in the case where a parameter passed to a method results in a null) we are verifying the code does throw this exception. If code were written to include a check (e.g. parameter != null), this would lead to a fail. So, would it be correct to then check for the expected exception thrown when the parameter is not null?
I am testing this within a J2EE environment and I also get an error from the EJB even though the unit tests pass?