We isolated the plasmonic contribution to surface-enhanced Raman scattering (SERS) and found it to be much stronger than expected. Organic dyes encapsulated in single-walled carbon nanotubes are ideal probes for quantifying plasmonic enhancement in a Raman experiment. The molecules are chemically protected through the nanotube wall and spatially isolated from the metal, which prevents enhancement by chemical means and through surface roughness. The tubes carry molecules into SERS hotspots, thereby defining molecular position and making it accessible for structural characterization with atomic-force and electron microscopy. We measured a SERS enhancement factor of 106 on α-sexithiophene (6T) molecules in the gap of a plasmonic nanodimer. This is two orders of magnitude stronger than predicted by the electromagnetic enhancement theory (104). We discuss various phenomena that may explain the discrepancy (including hybridization, static and dynamic charge transfer, surface roughness, uncertainties in molecular position and orientation), but found all of them lacking in enhancement for our probe system. We suggest that plasmonic enhancement in SERS is, in fact, much stronger than currently anticipated. We discuss novel approaches for treating SERS quantum mechanically that appear promising for predicting correct enhancement factors. Our findings have important consequences on the understanding of SERS as well as for designing and optimizing plasmonic substrates