We designed and implemented an experimental methodology to investigate gas hydrate formation and growth around a water-guest meniscus in a thin glass capillary, thus mimicking pore-scale processes in sediments. The glass capillary acts as a high-pressure optical cell in a range of supercooling conditions from 0.1 °C, i.e., very close to hydrate dissociation conditions, to ∼35 °C, very near the metastability limit. Liquid or gaseous CO2 is the guest phase in most of the experiments reported in this paper, and N2 in a few of them. The setup affords detailed microscopic observation of the roles of the key parameters on hydrate growth and interaction with the substrate: supercooling and substrate wettability. At low supercooling (less than 0.5 °C), a novel hydrate growth process is discovered, which consists of a hollow crystal originating from the meniscus and advancing on the guest side along the glass, fed by a thick water layer sandwiched between the glass and this crystal.