Electronic transitions from one excited state to another excited state of different spin symmetry play important roles in many biochemical reactions. Although recent years have seen much progress in the elucidation of nonradiative (intersystem crossing) relaxation mechanisms for such transitions, there is presently a scarcity of data available to assess whether also radiative (phosphorescence) mechanisms are relevant for these processes. Here, we demonstrate that the well-established ability of quantum chemical methods to describe intersystem crossing events between excited states can be supplemented by the ability to also describe inter-excited-state phosphorescence. Specifically, by performing four-component relativistic time-dependent density functional theory calculations, we obtain rate constants for the radiative transitions from the absorbing (1)(pi(H)pi(L)*) singlet state of lumiflavin to the (3)(pi(H)pi(L)*), (3)(n(N2)pi(L)*), and (3)(pi(H-1)pi(L)*) triplet states, and subsequently, we compare these results with rate constants calculated for the corresponding nonradiative transitions. Thereby, it is found that the radiative rate constants for these particular transitions are typically 2 to 5 orders of magnitude smaller than the nonradiative ones.