Context. Evolutionary models are widely used to infer the mass of stars, brown dwarfs, and giant planets. Their predictions are thought to be less reliable at young ages (< 200 Myr) and in the low-mass regime (< 1 M☉). GJ 2060 AB and TWA 22 AB are two rare astrometric M-dwarf binaries, respectively members of the AB Doradus (AB Dor) and Beta Pictoris (β Pic) moving groups. As their dynamical mass can be measured to within a few years, they can be used to calibrate the evolutionary tracks and set new constraints on the age of young moving groups. Aims: We provide the first dynamical mass measurement o