Remember however, if you can observe it and test it, it ain't supernatural by definition.
Is the rest of the world supposed to accept this as the only valid definition of what is, or is not, supernatural? If so, why? By what authority do you make this proposition, and with what evidence?
Test it, but not observe it. If you had seen Jesus walk on water you would have observed the supernatural, but you would not have been able to test it.
That said, I agree that science is limited in its value precisely because it can not be applied to the supernatural, among other things. But to tell a scientist that he may not consider the supernatural is to limit him unfairly.
Doyle had Sherlock Holmes say something like, "When you have eliminated all the alternatives, whatever remains, no matter how improbable, is not only probable, but the solution." (Apologies to Doyle.) I would be very disappointed in a scientist who moved to the supernatural before exhausting all possible alternatives and without a healthy dose of skepticism. I would be very disappointed in a scientist who, when faced with the supernatural being the only explaination (Jesus walking on water, for example) he would refuse that answer.
Shalom.