The influence of confinement on the persistence length of dsDNA molecules under a high ionic strength environment was explored by coarse-grained Monte Carlo simulations in channels of different profiles. It was found that under confinement three definitions of the persistence length of DNA molecules were not equivalent and represented different properties. In case of the global quantities, the projection and the WLC persistence lengths, the apparent values up to several hundred nanometres are observed for DNA confined in narrow channels. The orientational correlation function 〈cos θ(s)〉 of confined DNA shows a complex pattern, distinctive for semiflexible polymers. At weak and moderate confinements the function 〈cos θ(s)〉 suggests an unexpected increase in the apparent DNA flexibility. The orientational persistence length computed from the initial slope of the function 〈cos θ(s)〉 mirrors only short-scale correlations and gives the value close to the intrinsic persistence length of DNA. The simulation data of direct relevance to experimental studies of DNA in microfluidic devices are compared with analytical theories for stiff chains.