Proxima b is a potentially rocky exoplanet that lies in the habitable zone of Proxima Centauri. Given the activity of its M-Dwarf host, it is uncertain if Proxima b has retained an atmosphere or what any atmosphere might be like. Thus, it provides an important baseline for the types of atmospheres we can expect around M-Dwarfs and a crucial independent data point to compare to the possible atmospheres of other similar planets, like those in orbit of TRAPPIST-1. Together, these will provide us with a first indication on the prevalence of habitable planets in the galaxy. Several instruments have proposed to characterize Proxima b's atmosphere by leveraging the spatial resolution of the ELT to resolve it from Proxima Centauri and extract the faint spectrum of the exoplanet from the glare of its host star. The planet's spectrum will be extracted at high spectral resolution using the molecule mapping technique and, combined, the instruments of the ELT will disentangle the planet's reflective and thermal properties. In this presentation, I will show detailed simulations of HARMONI/ELT which demonstrate the feasibility of characterizing the reflected light of an Earth-like Proxima b. Additionally, I will show initial work on similarly detailed simulations at longer wavelengths for observations with METIS/ELT and discuss what synergies these may have with each other and with ANDES/ELT. Finally, I will discuss possible observing strategies to make the most of this unique target.