  We have studied the microwave electrodynamics of single crystal iron-based
superconductors Ba$_{0.72}$K$_{0.28}$Fe$_2$As$_2$ (hole-doped, $T_\mathrm{c}$
$\approx $30 K) and Ba(Fe$_{0.95}$Co$_{0.05}$)$_2$As$_2$ (electron-doped,
$T_\mathrm{c}$ $\approx$20 K), by cavity perturbation and broadband
spectroscopy. SQUID magnetometry was 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
$\Delta\lambda(T)$, and therefore the superfluid phase stiffness
$\lambda^2(0)/\lambda^2(T)$ 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
$\lambda^2(0)/\lambda^2(T)$ $\sim$ $T^n$ and \emph{n} $\approx$ 2.5. In the
three samples we studied, a weak feature near the sensitivity limit of our
measurements appears near $T/T_\mathrm{c}$ =~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 \FeAs
samples can be made to scale as $\omega^2$ 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 $\Delta\lambda(T)$.
