  Angular momentum loss by the plasma wind is considered as a universal feature
of isolated neutron stars including magnetars. The wind nebulae powered by
magnetars allow us to compare the wind properties and the spin-evolution of
magnetars with those of rotation-powered pulsars (RPPs). In this paper, we
construct a broadband emission model of magnetar wind nebulae (MWNe). The model
is similar to past studies of young pulsar wind nebulae (PWNe) around RPPs, but
is modified for the application to MWNe that have far less observational
information than the young PWNe. We apply the model to the MWN around the
youngest ($\sim$ 1kyr) magnetar 1E 1547.0-5408 that has the largest spin-down
power $L_{\rm spin}$ among all the magnetars. However, the MWN is faint because
of low $L_{\rm spin}$ of 1E 1547.0-5408 compared with the young RPPs. Since
most of parameters are not well constrained only by an X-ray flux upper limit
of the MWN, we adopt the model parameters from young PWN Kes 75 around PSR
J1846-0258 that is a peculiar RPP showing magnetar-like behaviors. The model
predicts $\gamma$-ray flux that will be detected in a future TeV $\gamma$-ray
observation by {\it CTA}. The MWN spectrum does not allow us to test hypothesis
that 1E 1547.0-5408 had milliseconds period at its birth because the particles
injected early phase of evolution are suffered from severe adiabatic and
synchrotron losses. Further both observational and theoretical studies of the
wind nebulae around magnetars are required to constrain the wind and spin-down
properties of magnetars.
