We have studied the microwave electrodynamics of single-crystal iron-based superconductors Ba0.72 K0.28 Fe2 As2 (hole doped, Tc30K) and Ba (Fe0.95 Co0.05) 2 As2 (electron doped, Tc20K), by cavity perturbation and broadband spectroscopy. Meissner curves were used to confirm the quality and homogeneity of the samples under study. Through cavity perturbation techniques, the temperature dependence of the in-plane London penetration depth Δλ (T), and therefore the superfluid phase stiffness λ2 (0) / λ2 (T) was measured. Down to 0.4 K, the data do not show the exponential saturation at low temperatures expected from a singly, fully gapped superconductor. Rather, both the electron- and the hole-doped systems seem to be best described by a power-law behavior with λ2 (0) / λ2 (T) ∼ Tn and n2.5. In the three samples we studied, a weak feature near the sensitivity limit of our measurements appears near T/ Tc =0.04, hinting at a corresponding low-energy feature in the superconducting density of states. The data can also be relatively well described by a simple two-gap s -wave model of the order parameter but this yields parameters which seem unrealistic and dependent on the fit range. Broadband surface resistance measurements reveal a sample-dependent residual loss whose origin is unclear. The data from the Ba0.72 K0.28 Fe2 As2 samples can be made to scale as ω2 if the extrinsic loss is treated as an additive component, indicating large scattering rates. Finally, the temperature dependence of the surface resistance at 13 GHz obeys a power law very similar to those observed for Δλ (T). © 2010 The American Physical Society.