A theory of the anomalous microwave conductivity and surface resistance of high-temperature superconductors is developed for a nested Fermi surface. The damping $\ensuremath{\Gamma}$ is derived for electron collisions across nearly parallel orbit segments. Above the superconducting temperature $\ensuremath{\Gamma}(\ensuremath{\omega},T)$ is linear in frequency $\ensuremath{\omega}$ and temperature T, in accord with the anomalous non-Drude conductivity which differentiates high-${T}_{c}$ cuprates from conventional metals. In the superconducting state a d-wave energy gap suppresses the damping---by reducing available scattering states---and thus explains why the YBCO microwave surface resistance ${R}_{s}$ drops so dramatically when the temperature is a few degrees below ${T}_{c}=90$ K. Numerical calculations of the infrared conductivity, reflectivity, microwave ${R}_{s},$ and penetration depth are presented, and comply with the YBCO experimental data if the gap has a large maximum value ${\ensuremath{\Delta}}_{\mathrm{dm}}\ensuremath{\simeq}{4T}_{c}.$ The cuprate spectral shapes differ notably from conventional BCS theory.
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