We present observations of the pulsar-wind nebula ( PWN ) region of SNR 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 _ { \nu } \propto \nu ^ { - \alpha _ { \nu } } , with the spectral index \alpha _ { \nu } = 0.17 \pm { 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 To conclude how this joins the synchrotron spectrum at higher frequencies we include hitherto unpublished AKARI mid-infrared data , and evaluate published data in the ultraviolet ( UV ) , optical and infrared ( IR ) .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 _ { \nu } = 0.87 ^ { +0.08 } _ { -0.10 } . There is room for 2.5 \times 10 ^ { -3 } ~ { } { M } _ { \odot } of dust with temperature \sim 55 K if there are dual breaks in the synchrotron spectrum , one around \sim 9 \times 10 ^ { 10 } Hz , and another at \sim 2 \times 10 ^ { 13 } Hz . The spectral index then changes at \sim 9 \times 10 ^ { 10 } Hz from \alpha _ { \nu } = 0.14 \pm 0.07 in the radio , to \alpha _ { \nu } = 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 \sim 1 \hbox { $ . ^ { \prime \prime } $ } 5 south-west of the pulsar , seen at other wavelengths , and resolved in the 3-cm data with its 0 . ^ { \prime \prime } 8 spatial resolution , is also strong in the millimeter range . The ACA data clearly reveal the supernova remnant shell \sim 20 - 35 \arcsec west of the pulsar , and for the shell we derive \alpha _ { \nu } = 0.64 \pm { 0.05 } for the range 8.6 - 145 GHz .