  It has been widely argued that Type-I super-luminous supernovae (SLSNe-I) are
driven by powerful central engines with a long-lasting energy injection after
the core-collapse of massive progenitors. One of the popular hypotheses is that
the hidden engines are fast-rotating pulsars with a magnetic field of
$B\sim{10}^{13}-{10}^{15}$ G. Murase, Kashiyama & Meszaros (2016) showed that
quasi-steady radio/submm emission from non-thermal electron-positron pairs in
nascent pulsar wind nebulae can be used as a counterpart of such pulsar-driven
supernovae (SNe). In this work, focusing on the nascent SLSN-I remnants, we
examine constraints that can be placed by radio emission. We show that the
Atacama Large Millimeter/submillimetre Array (ALMA) can detect the radio nebula
from SNe at $D_{\rm L} \sim 1 \ \rm Gpc$ in a few years after the explosion,
while the Jansky Very Large Array (VLA) can also detect the counterpart in a
few decades. The proposed radio followup observation could solve the parameter
degeneracy in the pulsar-driven SN model for optical/UV light curves, and could
also give us clues to young neutron star scenarios for SLSNe-I and fast radio
bursts.
