The work reported here represents a study into the total fluorescence exhibited by a broad selection of model, extremophilic and photosynthetic bacterial strains, over a great range of excitation and emission wavelengths from ultraviolet (UV) through visible to near infrared. The aim is to identify distinctive fluorescent features that may serve as detectable biosignatures of remnant microbial life on the Martian surface. A lab-bench fluorescence spectrometer was used to generate an excitation-emission matrix (EEM) for the unpigmented Escherichia coli, radiation-resistant Deinococcus radiodurans, Antarctic Dry Valley isolates Brevundimonas sp. MV.7 and Rhodococcus sp. MV.10, and the cyanobacterium Synechocystis sp. PCC 6803. Detailed EEMs, representing the fluorescence signature of each organism, are presented, and the most significant features suitable for biosignature surveys are identified, including small-molecule cellular metabolites, light-harvesting photosynthetic pigments and extracellular UV-screening compounds. E. coli exhibits the most intense emission from tryptophan, presumably due to the absence of UV-screening pigments that would shield the organism from shortwavelength light-exciting intracellular fluorescence. The efficacy of commonly available laser diodes for exciting cellular fluorescence is treated, along with the most appropriate filter wavelengths for imaging systems. The best combination of available laser diodes and PanCam filters aboard the ExoMars probe is proposed. The possibility of detecting fluorescence excited by solar UV radiation in freshly exposed surface samples by imaging when both sunlit and shadowed, perhaps by the body of the rover itself, is discussed. We also study how these biological fluorophore molecules may be degraded, and thus the potential biosignatures erased, by the high flux of far-ultraviolet light on Mars.