The distillative evaporation of a single levitated microdroplet composed of a mixture of 1-iodododecane and 1-bromotetradecane was followed by means of Raman spectroscopy to determine the time-dependent chemical composition and to explore the effects of morphology-dependent resonances (MDRs) on the Raman data. Additional measurements of the single-component evaporation rates were performed to obtain the parameters needed to analyze the binary droplet data. The enhancement of Raman signals by MDRs is analyzed and interpreted by means of Mie theory to determine the modes and optical characteristics which produce such enhancement. It is shown that only a limited number of all possible resonances produce the effect and that enhancement is very sensitive to the magnitude of the imaginary part of the complex refractive index. The narrowest resonances are damped and do not lead to Raman enhancement. Such analysis together with observation of the resonance modes which produce Raman enhancement make it possible to estimate the magnitude of the imaginary component of the refractive index. Multi-component evaporation theory is coupled with light-scattering theory to predict the size and refractive index of a distilling binary aerosol droplet. Predicted enhancements and measured Raman signals are shown to be in good agreement.