  Surface aging phenomena are discussed for semi-infinite systems prepared in a
fully disordered initial state and then quenched to or below the critical
point. Besides solving exactly the semi-infinite Ising model in the limit of
large dimensions, we also present results of an extensive numerical study of
the nonequilibrium dynamical behavior of the two-dimensional semi-infinite
Ising model undergoing coarsening. The studied models reveal a simple aging
behavior where some of the nonequilibrium surface exponents take on values that
differ from their bulk counterparts. For the two-dimensional semi-infinite
Ising model we find that the exponent $b_1$, that describes the scaling
behavior of the surface autocorrelation, vanishes. These simulations also
reveal the existence of strong finite-time corrections that to some extent mask
the leading scaling behavior of the studied two-time quantities.
