We determine ages for young supernova remnants in the starburst galaxi
es M82 and NGC 253 by applying Chevalier's model for radio emission fr
om supernova blast waves expanding into the ejecta of their precursor
stars. Absolute ages are determined by calibrating the model with radi
o observations of Cas A. We derive supernova rates of 0.10 and 0.08 yr
-1 for M82 and NGC 253, respectively. Assuming L(FIR) to be proportion
al to the supernova rate, we find r(SN) almost-equal-to 2 x 10(-12) x
LFIR, . yr-1 for these archetypal starburst galaxies. This approach is
unique in that the supernova rate is derived from direct observation
of supernova remnants rather than from star formation rates and an ass
umed initial mass function (IMF). We suggest that the approach present
ed here can be used to derive star-formation rates that are more direc
tly related to observable quantities than those derived by other metho
ds. We find that the supernova rate, FIR luminosity, and dynamical mas
s of the M82 starburst place few constraints on the IMF slope and mass
limits.