The electronic absorption spectra of the bis(porphyrin) sandwich complexes of the metals Zr, Ce, and Th are studied with time-dependent density functional theory (TIDDIFT). A ground-state electronic structure analysis reveals that the highest occupied one-electron levels are, as expected, composed of the porphyrin a(1u) and a(2u) highest occupied orbitals (the Gouterman orbitals), but the level pattern is not simply a pair of low-lying nearly degenerate in-phase combinations and a pair of high-lying approximately degenerate antibonding combinations. Instead, the a(1u) split strongly and the a(2u) do not. Since the calculated spectrum agrees very well with experiment, the assignment leaves little doubt that although the experimental spectrum has porphyrin-like features, such as the well-known Q and B bands, the actual composition of the states is rather different from that in porphyrin. In particular the strong mixing of a(1u) --> e(g)* and a(2u) --> e(g)* is absent, there is mixing with excitations of non-Gouterman type, and, in Ce, ring to metal charge-transfer transitions play an important role. The composition of the states as calculated in this work does not lead to a classification of the excitations as purely "excitonic" or "charge-resonance".