We show how, via resonant tunneling, a tight binding model of a molecular adsorbate might be used to account for the anomalous conductance observed in STM images of many molecular adsorbates. New calculations show that even strong binding to the substrate does not necessarily destroy a resonance. Electrochemistry can be used to make biomolecular adsorbates that can be imaged by STM reliably. Current‐distance and current‐voltage data obtained over DNA‐salt complexesinsuitshow that the charge transport is most likely by tunneling and that the electronic properties of the tunnel gap are very different over a molecular adsorbate when compared with a gap that contains just small inorganic contaminants. In particular, conductance over the organic adsorbate is greatly enhanced. The electronic properties of the adsorbate are strongly affected by the position of the STM tip, demonstrating that electronic states might be altered by the stress applied by the STM tip under the control of the STM servo. This provides a mechanism to bring about a resonance or to bring a state close enough to resonance so that the set‐point tunnel conductance is achieved.