The current-voltage characteristics of a voltage-biased Josephson junction in the low conductance regime of an ultra-low temperature scanning tunneling microscope (STM) is dominated by sequential charge tunneling. Using P(E) theory we show that the Josephson coupling energy, experimentally determined in this regime, is in good agreement with the critical current I-0 calculated from the Ambegaokar-Baratoff formula. In this way, we can determine the critical current values of a Josephson junction in an STM. Furthermore, we experimentally determine a range of validity for P(E) theory, which is in accordance with theoretical predictions. In this way, we establish an optimal parameter range, in which Josephson STM can be performed.