  The London penetration depth for the unconventional superconductor
Sr$_2$RuO$_4$ is analyzed assuming an order parameter which breaks time
reversal symmetry and parity simultaneously. Such a superconducting state
possesses chiral quasiparticle states with subgap energies at the surface. We
show that these subgap states can give a significant contribution to the
low-temperature behavior of the London penetration depth yielding a $ T^2 $
power-law even though bulk quasiparticle spectrum is gapped. The presence of
several electron bands gives rise to interband transition among the subgap
surface states and influences the properties of the surface impedance.
Furthermore, the surface states lead also to a non-linear Meissner effect.
