  Magnetars have been considered as progenitors of magnetar giant flares (MGFs)
and fast radio bursts (FRBs). We present detailed studies on afterglow
emissions caused by bursts that occur in their wind nebulae and surrounding
baryonic ejecta. In particular, following the bursts-in-bubble model proposed
by Murase, Kashiyama \& M\'esz\'aros, we analytically and numerically calculate
spectra and light curves of such afterglow emission. We scan parameter space
for the detectability of radio signals, and find that a burst with
$\sim10^{45}~{\rm erg}$ is detectable with the Very Large Array or other
next-generation radio facilities. The detection of multi-wavelength afterglow
emission from MGFs and/or FRBs is of great significance for their localization
and revealing their progenitors, and we estimate the number of detectable
afterglow events.
