The LHCb collaboration at CERN studies heavy-flavour hadrons produced at the Large Hadron Collider. For the Upgrade II of the LHCb detector, foreseen to operate from 2036 in LHC Run 5, the current Scintillating-Fibre (SciFi) tracker will be replaced by the Mighty Tracker, combining silicon pixels in the innermost region and scintillating fibres in the outer region. In this environment, higher radiation levels and occupancies require improved scintillating-fibre technology with enhanced light collection, timing performance, and radiation tolerance. This thesis focuses on the development and characterisation of silicon photomultipliers (SiPMs) for the Mighty SciFi detector. Microlens arrays have been designed and optimised using dedicated optical simulations and subsequently implemented on customised SiPM arrays. The simulation predicts a significant increase in light collection up to $25%$ with respect to conventional coated SiPMs. Measurements of the photon detection efficiency confirm the expectations and reveal a reduction in optical cross-talk as well. The single-photon time resolution of SiPMs from different manufacturers, considered for the upgrade, has also been measured, with the best sensors achieving values down to 75 ps FWHM. The performance of \SI{2.4}{m} long scintillating-fibre mats read out with conventional and microlens-enhanced SiPMs has been studied in test-beam campaigns at CERN. Microlens-enhanced sensors provide a gain in light yield of $20-25%$, in agreement with simulation results. This translates into an average improvement of about $15%$ in time resolution, with values between \SI{250}{ps} and \SI{500}{ps} obtained for SiPMs coupled to a six-layer fibre mat. The performance of a thinner four-layer mat, which has the advantage of reduced material budget and cluster size but a lower light output, has also been assessed. In addition, the radiation-induced increase in dark count rate of all 4096 SiPMs installed in the current LHCb SciFi Tracker has been monitored during LHC Run 3. A linear dependence on delivered luminosity is observed, together with significant annealing effects after warm-up periods, leading to a reduction of the dark count rate by a factor of up to three. These measurements validate the expected radiation-damage behaviour and provide input for future detector operation and performance studies. The results presented in this thesis demonstrate that microlens enhancement is an effective solution to improve the light yield and timing performance of scintillating-fibre detectors, and provide a detailed assessment of radiation effects in large-scale SiPM systems. These developments constitute important steps toward the implementation of the Mighty SciFi detector for LHCb Upgrade II.