Raman spectroscopy is a powerful technique that enables fingerprinting of materials, molecules, and chemical environments by probing vibrational resonances. In many applications the desired Raman signals are masked by fluorescence, either from the molecular system being studied, or from adjacent metallic nanostructures. Here we show that wavelength-modulated Raman spectroscopy provides a powerful way to significantly reduce the strength of the fluorescence background, thereby allowing the desired Raman signals to be clearly recorded. We make use of this approach to explore Raman scattering in the context of vibrational strong coupling, an area that has thus far been problematic to visualise. Specifically we look at strong coupling between the vibrational modes in a polymer and two types of confined light field, the fundamental mode of a metal-clad microcavity, and the surface-plasmon modes of an adjacent thin metal film. Whilst we find clear advantages in using the wavelength-modulated Raman approach, our results on strong coupling are inconclusive, and highlight the need for more work in this exciting topic area.