Mesoporous silica phases, with uniform pores of dimensions in the 2-30 nm range, offer a uniquely well-defined environment for the study of the effects of two-dimensional spatial confinement on the properties of glass-forming liquids. We report observations by differential scanning calorimetry of the vitrification of o-terphenyl (OTP), salol, and glycerol in hexagonal mesoporous silica (MCM-41 and SBA-15) in a wide range of pore sizes from 2.6 to 26.4 nm. In agreement with previous studies, where a controlled porous glass is used as a solid matrix, the glass transition temperature for o-terphenyl diminishes with decreasing pore size. In contrast to OTP, glycerol shows a gradual increase in glass transition temperature, while in salol a slight reduction of glass transition temperature is observed, followed by an increase, which results in glass transition temperature indistinguishable from that of the bulk for the smallest pores. These results are discussed in terms of liquid-surface interactions in an interfacial layer, monitored by Fourier-transformed infrared spectroscopy in the study. The hydrogen bonding with silica surface silanols dominates the glass transition trends observed in salol and glycerol.