The photophysics and excited-state dynamics of two dyads consisting of either a free-base or a zinc-tetraphenylporphyrin linked through a rigid bridge to a core-substituted naphthalenediimide (NDI) have been investigated by femtosecond-resolved spectroscopy. The absorption and fluorescence spectra differ substantially from those of the individual units, pointing to a substantial coupling and to a delocalisation of the excitation over the whole molecule, as confirmed by quantum chemistry calculations. A strong dependence of their excited-state dynamics on the solvent polarity has been observed. In toluene, the fluorescence quantum yield of the dyads is of the order of a few percent and the main decay channel of the emitting state is proposed as intersystem-crossing to the triplet state. However, in a medium polarity solvent like dichloromethane, the emitting state undergoes charge separation from the porphyrin to the NDI unit within 1-3 ps, and the ensuing charge-separated state recombines in about 10-20 ps. This solvent dependence can be explained by the weak driving force for charge separation in polar solvents and the large electronic coupling between the porphyrin and NDI moieties, making charge separation a solvent-controlled adiabatic process.