I don't think JWST could even resolve it from its parent star, judging by [0]. They're too close together.
Proxima Centauri has a luminosity of 0.0017 suns [1], so Earth-like conditions would occur at ~sqrt(0.0017) au = 0.04 au, an apparent angular separation of arcsin(0.04 au / 4.2 light years) = 0.03". JWST wants star-planet separations at least an order of magnitude larger [0], ideally with very hot, infrared-bright planets.
E-ELT should be able to resolve them, according to [2]. Page 7 gives values for a very similar scenario: an Earth-like planet around an M dwarf (like Proxima), 6 pc away (5 times farther), at an angular separation of 0.015" (half as wide). In this scenario, E-ELT could image the star and planet as separate points, and take useful spectroscopic measurements of the planet's light. For it example it could detect a spectral line of oxygen (O2) in 4 hours of exposure time.
Proxima Centauri has a luminosity of 0.0017 suns [1], so Earth-like conditions would occur at ~sqrt(0.0017) au = 0.04 au, an apparent angular separation of arcsin(0.04 au / 4.2 light years) = 0.03". JWST wants star-planet separations at least an order of magnitude larger [0], ideally with very hot, infrared-bright planets.
E-ELT should be able to resolve them, according to [2]. Page 7 gives values for a very similar scenario: an Earth-like planet around an M dwarf (like Proxima), 6 pc away (5 times farther), at an angular separation of 0.015" (half as wide). In this scenario, E-ELT could image the star and planet as separate points, and take useful spectroscopic measurements of the planet's light. For it example it could detect a spectral line of oxygen (O2) in 4 hours of exposure time.
[0] http://nexsci.caltech.edu/workshop/2016/NIRCam_Planets_and_B...
[1] https://en.wikipedia.org/wiki/Proxima_Centauri
[2] https://www.eso.org/sci/meetings/2014/exoelt2014/presentatio...