We evaluate the potential of a hand-held energy dispersive XRF spectrometer for the preliminary classification of non-chondritic differentiated meteorites. The studied achondrites include nine lunar meteorites, seventeen Martian meteorites, five angrites and eighteen meteorites from asteroid 4 Vesta. Analytical precision and accuracy was tested on thirty-nine terrestrial igneous rock slabs with a wide range of composition. Replicate analyses, performed on the studied meteorites, show that Fe/Mn values together with Si and Ca/K ratio can be used in the discrimination of different achondrite groups. Fusion crust's Fe/Mn values of meteorites from Vesta and Mars are indistinguishable from those of the interior implying that even measurements on the fusion-crusted external surface could be sufficient to pigeonhole non-chondritic meteorites. Hand-held energy dispersive XRF spectrometer is a non-destructive but very effective technique for preliminary classification of achondrites in the field and in laboratory and for the identification of mislabelled meteorites in museum collections