We present observations of the pulsar-wind nebula (PWN) region ofSNR 0540-69.3. The observations were made with the Atacama Compact Array (ACA) in Bands 4 and 6. We also add radio observations from the Australia Compact Array (ATCA) at 3 cm. For 1.449 - 233.50 GHz we obtain a synchrotron spectrum $F_{ u} propto u^{-alpha_{ u}}$, with the spectral index $alpha_{ u} = 0.17pm{0.02}$. To conclude how this joins the synchrotron spectrum at higher frequencies we include hitherto unpublished AKARI mid-infrared data, and evaluate published data in the ultraviolet (UV), optical and infrared (IR). In particular, some broad-band filter data in the optical must be discarded from our analysis due to contamination by spectral line emission. For the UV/IR part of the synchrotron spectrum, we arrive at $alpha_{ u} = 0.87^{+0.08}_{-0.10}$. There is room for $2.5times10^{-3}$ solar masses of dust with temperature $sim 55$ K if there are dual breaks in the synchrotron spectrum, one around $sim 9times10^{10}$ Hz, and another at $sim 2times10^{13}$ Hz. The spectral index then changes at $sim 9times10^{10}$ Hz from $alpha_{ u} = 0.14pm0.07$ in the radio, to $alpha_{ u} = 0.35^{-0.07}_{+0.05}$ in the millimetre to far-IR range. The ACA Band 6 data marginally resolves the PWN. In particular, the strong emission 1.5 south-west of the pulsar, seen at other wavelengths, and resolved in the 3-cm data with its 0.8 spatial resolution, is also strong in the millimeter range. The ACA data clearly reveal the supernova remnant shell 20-35 arcsec west of the pulsar, and for the shell we derive $alpha_{ u} = 0.64pm{0.05}$ for the range $8.6-145$~GHz.
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