This thesis attempts to answer the question: what is the superconducting mechanism in e-iron and CeCu2Si2? There are many reasons to think that it is not a conventional BCS-type mechanism in either system. Pressure enables us to continuously vary the electronic properties of a material, and fluctuations between different electronic configurations at a quantum instability are likely to cause the superconducting pairing. Transport and calorimetry measurements were carried out in steatite and helium pressure media. The most likely pairing mechanism in Fe is that mediated by magnetic fluctuations, and we have concluded that there is a strong possibility of e-Fe being a ferromagnetically mediated spin-triplet superconductor. While it is widely accepted that in CeCu2Si2 the superconductivity at ambient pressure is mediated by antiferromagnetic spin fluctuations, we conclude that a new mechanism is responsible for the pairing at high pressure, with the attractive interaction based on the exchange of valence fluctuations.