Two series of measurements were performed in the JSI TRIGA research reactor in 2014 and 2017 to validate the 55Mn(n,γ)56Mn cross-sections and experimentally investigate the relationship between the 55Mn(n,γ)56Mn reaction and the rate of tritium production through the 6Li(n,t)4He reaction. Indeed, previously observed similarities between the sensitivity profiles of the neutron reaction of tritium production on lithium, 6Li(n,t)4He, and those of the 55Mn(n,γ)56Mn reaction in tritium breeder modules indicated that the latter reaction could be used as an effective monitor of tritium production, at least for short-term monitoring (the half-life of 56Mn being 2.579 h). However, experimental verification, improvements and validation of the 55Mn(n,γ)56Mn cross-sections are needed in order to meet the required accuracy. Foils of certified reference material Al-1%Mn, as well as LiF thermoluminescent detectors and Li2O samples were irradiated, both bare and under cadmium, to study the potential use of the 55Mn(n,γ)56Mn reaction for monitoring tritium production in fusion devices. Additionally, Al-0.1%Au was also irradiated for comparison, the 197Au(n,γ)198Au reaction cross-section being a standard. In order to obtain complementary information for data validation purposes, the irradiations were performed in positions within the JSI TRIGA reactor with different neutron spectra, i.e. in the central channel, the pneumatic tube and the F19 position, both in the outer 'F' ring of the reactor core and in the IC-40 irradiation channel located in the graphite reflector surrounding the reactor core. Bare and cadmium-covered irradiations were needed to subtract the contribution of epithermal neutrons to the 55Mn(n,γ)56Mn reaction. Calculations of the reaction rates were performed using the Monte Carlo code MCNP6.1 with a detailed model of the JSI TRIGA reactor, with the samples, the irradiation capsules and covers being modelled explicitly. The uncertainties involved in the measurements and the calculations were carefully evaluated. The principal objective was to study the energy response and correlations between the 55Mn(n,γ)56Mn reaction in irradiated Al-1%Mn and the 6Li(n,t)4He reaction in irradiated LiF and Li2O. Good consistency between the measured and calculated 55Mn(n,γ)56Mn and 197Au(n,γ)198Au reaction rates, in most cases within the uncertainty bars, was observed.