A fully quantitative theory connecting protein conformation and optical spectroscopy would facilitate deeper insights into biophysical and simulation studies of protein dynamics and folding. The web server DichroCalc (http://comp.chem.nottingham.ac.uk/dichrocalc) allows one to compute from first principles the electronic circular dichroism spectrum of a (modeled or experimental) protein structure or ensemble of structures. The regular, repeating, chiral nature of secondary structure elements leads to intense bands in the far-ultraviolet (UV). The near-UV bands are much weaker and have been challenging to compute theoretically. We report some advances in the accuracy of calculations in the near-UV, realized through the consideration of the vibrational structure of the electronic transitions of aromatic side chains. The improvements have been assessed over a set of diverse proteins. We illustrate them using bovine pancreatic trypsin inhibitor and present a new, detailed analysis of the interactions which are most important in determining the near-UV circular dichroism spectrum.