We calculate the microwave conductivity of a d(x2-y2) superconductor i
n the presence of elastic impurity scattering and inelastic scattering
due to antiferromagnetic spin fluctuations. The low-temperature condu
ctivity does not simply reflect the linear temperature dependence of t
he number of quasiparticles in a d-wave system, as often supposed. We
compare with recent data on high-quality YBa2Cu3O6.95 single crystals.