We examine the influence of singlet-triplet intersystem crossing (ISC) and excited-state molecular relaxation on strong exciton-photon coupling in optical microcavities filled with small-molecular-weight organic materials. The effect of ISC is considered by comparing coupling effects in the phosphorescent organic platinum(II) octaethylporphyrin to those in the fluorescent free-base porphyrin tetraphenylporphyrin (TPP). The influence of excited-state molecular relaxation is studied by examining coupling to the Soret band of TPP. Both ISC and excited-state molecular relaxation prevent the population of polariton states under nonresonant optical excitation. The interplay between strong coupling and relaxation processes offers a unique opportunity to directly probe fundamental ultrafast excitonic phenomena. The competition between coupling in microcavities and these processes allows for estimation of their relative transition rates.