  Motivated by experiments on double quantum dots, we study the problem of a
single magnetic impurity confined in a finite metallic host. We prove an exact
theorem for the ground state spin, and use analytic and numerical arguments to
map out the spin structure of the excitation spectrum of the many-body
Kondo-correlated state, throughout the weak to strong coupling crossover. These
excitations can be probed in a simple tunneling-spectroscopy transport
experiment; for that situation we solve rate equations for the conductance.
