  We discuss how we can detect and identify counterparts of fast radio bursts
(FRBs) in future optical follow up observations of FRBs if real-time alert of
FRBs becomes available. We consider kilonovae as candidates of FRB optical
counterparts, as expected in the case that FRBs originate from mergers of
double neutron star binaries. Although theoretical predictions on luminosities
of kilonovae are still highly uncertain, recent models suggest that kilonovae
can be detected at redshifts up to z $\sim$ 0.3 within the range of the
uncertainties. We expect $\sim$ 1--5 unrelated supernovae (SNe) down to a
similar variability magnitude in 5 days interval within the typical error
radius of a FRB. We show that, however, a kilonova can be distinguished from
these SNe by its rapid decay and/or color evolution, making it possible to
verify the existence of a kilonova associated with a FRB. We also discuss the
case that SNe Ia are FRB optical counterparts, as it might be if FRBs originate
from double white dwarf binaries. Verification of this scenario is also
possible, since the chance probability of finding a SNe Ia having consistent
explosion time with that of a FRB within the FRB error region is small
(typically $\lesssim$ 0.01).
