  We study the ageing properties of the semi-infinite kinetic spherical model
at the critical point and in the ordered low-temperature phase, both for
Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation
ratio and the scaling functions of two-time surface correlation and response
functions are determined explicitly in the dynamical scaling regime. In the
low-temperature phase our results show that for the case of Dirichlet boundary
conditions the value of the non-equilibrium surface exponent $b_1$ differs from
the usual bulk value of systems undergoing phase ordering.
