Single-walled carbon nanotubes (SWCNTs) are noncovalently functionalised with octaethylporphyrins (OEPs) and the resulting nanohybrids are isolated from the free OEPs. Electron paramagnetic resonance (EPR) spectroscopy of cobalt(II)OEP, adsorbed on the nanotube walls by pi-pi-stacking, demonstrates that the CNTs act as electron acceptors. EPR is shown to be very effective in resolving the different interactions for metallic and semiconducting tubes. Moreover, molecular oxygen is shown to bind selectively to nanohybrids with semiconducting tubes. Water solubilisation of the porphyrin/CNT nanohybrids using bile salts, after applying a thorough washing procedure, yields solutions in which at least 99% of the porphyrins are interacting with the CNTs. Due to this purification, we observe, for the first time, the isolated absorption spectrum of the interacting porphyrins, which is strongly red-shifted compared to the free porphyrin absorption. In addition a quasi-complete quenching of the porphyrin fluorescence is also observed.