The tidal disruption of the Sagittarius dwarf Spheroidal galaxy (Sgr dSph) is producing the most prominent substructure in the Milky Way (MW) halo, the Sagittarius Stream. Aside from field stars, the Sgr dSph is suspected to have lost a number of globular clusters (GC). Many Galactic GC are suspected to have originated in the Sgr dSph. While for some candidates an origin in the Sgr dSph has been confirmed due to chemical similarities, others exist whose chemical composition has never been investigated. NGC 5053 and NGC 5634 are two among these scarcely studied Sgr dSph candidate-member clusters. To characterize their composition we analyzed one giant star in NGC 5053, and two in NGC 5634. We analize high-resolution and signal-to-noise spectra by means of the MyGIsFOS code, determining atmospheric parameters and abundances for up to 21 species between O and Eu. The abundances are compared with those of MW halo field stars, of "unassociated" MW halo globulars, and of the metal poor Sgr dSph main body population. We derive a metallicity of [FeII/H]=-2.26+/-0.10 for NGC 5053, and of [FeI/H]=-1.99+/-0.075 and -1.97+/-0.076 for the two stars in NGC 5634. This makes NGC 5053 one of the most metal poor globular clusters in the MW. Both clusters display an alpha enhancement similar to the one of the halo at comparable metallicity. The two stars in NGC 5634 clearly display the Na-O anticorrelation widespread among MW globulars. Most other abundances are in good agreement with standard MW halo trends. The chemistry of the Sgr dSph main body populations is similar to the one of the halo at low metallicity. It is thus difficult to discriminate between an origin of NGC 5053 and NGC 5634 in the Sgr dSph, and one in the MW. However, the abundances of these clusters do appear closer to that of Sgr dSph than of the halo, favoring an origin in the Sgr dSph system.