  We report on the effect of monochromatic microwave (MW) radiation on the weak
localization corrections to the conductivity of quasi-one-dimensional (1D)
silver wires. Due to the improved electron cooling in the wires, the MW-induced
dephasing was observed without a concomitant overheating of electrons over wide
ranges of the MW power $P_{MW}$ and frequency $f$. The observed dependences of
the conductivity and MW-induced dephasing rate on $P_{MW}$ and $f$ are in
agreement with the theory by Altshuler, Aronov, and Khmelnitsky \cite{Alt81}.
Our results suggest that in the low-temperature experiments with 1D wires,
saturation of the temperature dependence of the dephasing time can be caused by
an MW electromagnetic noise with a sub-pW power.
