Since the 2002 assignment of absorption and emission transitions to specific (n,m) structures, optical spectroscopy has offered the potential for simple, detailed structure-resolved characterization of SWCNT samples. However, this goal has not been fully realized because of incomplete spectroscopic and photophysical knowledge and a lack of specialized instrumentation. We describe here recent progress in overcoming these problems to enable quantitative sample analysis through combined fluorescence and absorption spectroscopy. One important step was determining absolute E11 absorption cross sections (molar absorptivities) for a number of common (n,m) species. This was achieved by using a direct counting method to calibrate the absolute concentrations of reference samples, and then by extending the list of measured cross sections through variance spectroscopy determinations of (n,m)-resolved particle concentrations in mixed samples. To properly interpret fluorimetric data, we have measured, interpreted, and modeled emission spectra and excitation spectra for a range of semiconducting (n,m) species. Combinations of single particle and ensemble spectroscopies were used for these studies. The models were extrapolated to other (n,m) species to predict E11 line widths and shapes plus the positions, amplitudes, and widths of spectral sidebands. When combined with data on structure-dependent fluorimetric efficiencies, the results allow fluorescence spectra of nanotube mixtures to be simulated as a sum of contributions from multiple (n,m) species of determined relative concentrations. To convert those concentrations from relative into absolute values, the absorption spectrum of a mixed sample is simulated as a background function plus components determined from the fluorescence emission and excitation profiles for the (n,m) species that were found to be present. Then the separate E11 (n,m) absorbance components are divided by their structure-specific absorption cross sections to find absolute species concentrations. The overall process allows quantitation of semiconducting (n,m) concentrations from simple and quick spectral measurements.