Water confined in narrow nanopores that prevent ice crystallization is usually studied as a means to understand the anomalous behavior of bulk liquid water. Nevertheless, there is no agreement on the similarity of the thermodynamics of bulk and nanoconfined liquid water, In this work, we use molecular dynamics simulations with the mW water model to investigate the phase behavior of liquid water in bulk and confined in a 1.5 nm cylindrical pore with water-surface interactions identical to water-water interactions. Through analysis of the isochors of bulk liquid water V(T,p) we extrapolate the locus of a putative liquid-liquid critical point (LLCP) in bulk mW water at 190 K and 1215 atm. This is a "virtual LLCP", as it would lie in a region of the phase diagram where fast crystallization of water impedes equilibration of the liquid. We find that confinement has a weak effect on the loci of the thermodynamic anomalies: the maxima in density and heat capacity of confined water occur at T,p similar to that in bulk. The heat capacity peak of confined water is due to a transformation within the confined liquid; we verify that ice does not form in the pores. Confined mW water presents a heat capacity maximum C(p)(max)(p) up to the highest pressure we investigated, 4000 atm. The magnitude of the heat capacity peak C(p)(max)(p) has a nonmonotonous dependence with pressure, attaining a maximum at conditions close to those of the locus of the bulk water's virtual LLCP. We do not find, however, direct evidence of a first-order liquid-liquid transition in confined water for pressures above or below the locus of the maximum response function. The extreme value of the response functions of confined water could be a rounded manifestation of an equivalent feature in the free energy surface of bulk water.