Geometrical effects influencing the measured spin coherence and quantum phase coherence in mesoscopic structures were characterized by low-temperature spin-dependent quantum transport experiments. The findings are of possible relevance for the design of devices for quantum technologies, and have foundational aspects as well. The materials studied have strong spin-orbit interaction and are heterostructures of InSb, InAs, or InGaAs, and the semimetal Bi with its surface states. The materials were patterned into mesoscopic stadia, narrow channels or quantum interferometers, of typical size ~ 1 micron, comparable to the spin and quantum phase coherence lengths. Aharonov-Bohm experiments, antilocalization, and universal conductance fluctuations were used to quantify the spin- and quantum phase coherence lengths. Using geometrical constraints on the accumulation of quantum geometric phases, the work shows a correspondence, in a diffusive transport regime, between mesoscopic dephasing effects due to time-reversal symmetry breaking by magnetic fields, and spin decoherence due to spin-orbit interaction (Aharonov-Bohm / Aharonov-Casher correspondence). The work also reveals device-geometrical influences on quantum phase coherence from coupling to the classical environment and geometrical effects of electron-electron interactions.