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 & Mészáros (2016), 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 ∼ 10 45 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.