We study the impact of experimental imperfections on a recently proposed protocol for performing quantum simulations of vibronic spectroscopy. Specifically, we propose a method for quantifying the impact of these imperfections, optimizing an experiment to account for them, and benchmarking the results against a classical simulation method. We illustrate our findings using a proof of principle experimental simulation of part of the vibronic spectrum of tropolone. Our findings will inform the design of future experiments aiming to simulate the spectra of large molecules beyond the reach of current classical computers.