Motivated by a recent experiment [C. Guo et al., Proc. Natl. Acad. Sci. U. S. A. 113, 10785 (2016)], we carry out a theoretical study of electron transport through peptide-based single-molecule junctions. We analyze the pristine hepta-alanine and its functionalizations with a single tryptophan unit, which is placed in three different locations along the backbone. Contrary to expectations from the experiment on self-assembled monolayers, we find that insertion of tryptophan does not raise the electrical conductance and that the resulting peptides instead remain insulating in the framework of a coherent transport picture. The poor performance of these molecules as conductors can be ascribed to the strongly off-resonant transport and low electrode-molecule coupling of the frontier orbitals. Although the introduction of tryptophan increases the energy of the highest occupied molecular orbital (HOMO) of the peptides in the gas phase, the new HOMO states are localized on the tryptophan unit and therefore essentially do not contribute to coherent charge transport.