Among the various factors influencing the charge transport through molecular electronic devices, changes in molecular conformation are of interest also because they do not have counterpart in traditional electronics. Out of the multitude of issues that are relevant from this perspective, in the present work we discuss aspects relevant for molecules forming self-assembled monolayers (SAMs) adsorbed on metallic electrodes in the limiting cases of low coverage and high coverage, respectively. The molecules to be examined, which are very common work-horses of molecular electronics, are in both cases easily deformable (“floppy”) species. In the former case, the specific molecule to be considered is azurin, an archetype of soluble redox proteins containing metal ions. Biphenylene monothiol and 4-(4-pyridinyl)benzenethiol, the specific molecules chosen for the analysis of the second case, are representative for the class of molecules consisting of two aromatic (benzene or benzene derivative) rings that can easily rotate relative to each other. The possibility to quantitatively describe the charge transport as a one-step coherent tunneling mechanism is the main aspect that will be emphasized in the former case. This is important because the charge transport in systems where molecular conformation substantially changes is commonly assumed to be a two-step hopping process and described within flavors of Marcus type formulas, which turned out to be invalidated by the azurin transport data examined. For high coverage situations, we present new results providing further support to our recent finding on the possibility to strongly enhance the twisting with respect to the situation of isolated molecules. Furthermore, we demonstrate that this twisting enhancement is not caused by the charge transfer at the metal-molecule interface. Rather, it represents an unusual effect of spatial confinement; although driven by the substrate metal, it can be theoretically modeled within a metal-free approach.