  We study the effective resistance of small-world resistor networks. Utilizing
recent analytic results for the propagator of the Edwards-Wilkinson process on
small-world networks, we obtain the asymptotic behavior of the
disorder-averaged two-point resistance in the large system-size limit. We find
that the small-world structure suppresses large network resistances: both the
average resistance and its standard deviation approaches a finite value in the
large system-size limit for any non-zero density of random links. We also
consider a scenario where the link conductance decays as a power of the length
of the random links, $l^{-\alpha}$. In this case we find that the average
effective system resistance diverges for any non-zero value of $\alpha$.
