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.