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 α < 0.3 (S v ∝ v α ) suggests the presence of non-thermal emission, probably originating in a colliding-wind region. A second, unrelated radio source was detected ∼10″ north of WR 21a at (RA, Dec) J2000 = (10 h 25 m 56 s .49, -57°48′34.4″), with flux densities of 0.36 and 0.55 mJy at 4.8 and 8.64 GHz, respectively, resulting in α = 0.72. H I observations in the area are dominated by absorption against the prominent H II 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.