This paper reports on magnetometry and magnetoresistance measurements of MnSi epilayers performed in out-of-plane magnetic fields. We present a theoretical analysis of the chiral modulations that arise in confined cubic helimagnets where the uniaxial anisotropy axis and magnetic field are both out-of-plane. In contrast to in-plane field measurements (Wilson et al., Phys. Rev. B 86, 144420 (2012)), the hard-axis uniaxial anisotropy in MnSi/Si(111) increases the energy of (111)oriented skyrmions and in-plane helicoids relative to the cone phase, and makes the cone phase the only stable magnetic texture below the saturation field. While induced uniaxial anisotropy is important in stabilizing skyrmion lattices and helicoids in other confined cubic helimagnets, the particular anisotropy in MnSi/Si(111) entirely suppresses these states in an out-of-plane magnetic field. However, it is predicted that isolated skyrmions with enlarged sizes exist in MnSi/Si(111) epilayers in a broad range of out-of-plane magnetic fields. These results reveal the importance of the symmetry of the anisotropies in bulk and confined cubic helimagnets in the formation of chiral modulations and they provide additional evidence of the physical nature of the A-phase states in other B20-compounds. 75.70.Ak