  We study the physics of a magnetic molecule described by a "giant" spin with
multiple ($d > 2$) spin states interacting with the quantized cavity field
produced by a superconducting resonator. By means of the input-output
formalism, we derive an expression for the output modes in the dispersive
regime of operation. It includes the effect of magnetic anisotropy, which makes
different spin transitions addressable. We find that the measurement of the
cavity transmission allows to uniquely determine the spin state of the qudits.
We discuss, from an effective Hamiltonian perspective, the conditions under
which the qudit read-out is a non-demolition measurement and consider possible
experimental protocols to perform it. Finally, we illustrate our results with
simulations performed for realistic models of existing magnetic molecules.
