  We study the conformal spectra of the critical square lattice Ising model on
the Klein bottle and M\"obius strip using Yang-Baxter techniques and the
solution of functional equations. In particular, we obtain expressions for the
finitized conformal partition functions in terms of finitized Virasoro
characters. This demonstrates that Yang-Baxter techniques and functional
equations can be used to study the conformal spectra of more general exactly
solvable lattice models in these topologies. The results rely on certain
properties of the eigenvalues which are confirmed numerically.
