We present results of high-resolution radio continuum observations towards the binary star WR 21a (Wack 2134) obtained with the Australia Telescope Compact Array (ATCA) at 4.8 and 8.64 GHz. We detected the system at 4.8 GHz (6 cm) with a flux density of 0.25+-0.06 mJy and set an upper limit of 0.3 mJy at 8.64 GHz (3 cm). The derived spectral index of alpha < 0.3 [S(nu)=k.nu**(alpha)] suggests the presence of non-thermal emission, probably originating in a colliding-wind region. A second,

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... ed radio source was detected ~10" north of WR 21a at (RA, Dec)(J2000)=(10h 25m 56.49, -57deg 48' 34.4", with flux densities of 0.36 and 0.55 mJy at 4.8 and 8.64 GHz, respectively, resulting in alpha = 0.72. HI observations in the area are dominated by absorption against the prominent HII region RCW 49. Analysis of a complete set of archived X-ray observations of WR 21a confirms its strong variability but throws into doubt previous suggestions by Reig (1999) of a period of years for the system. Finally, we comment on the association with the nearby EGRET source 3EG J1027-5817.