The anisotropic thermoelectric transport properties of bulk silicon strained in the [111]-direction were studied by detailed first-principles calculations focusing on a possible enhancement of the power factor. Electron and hole doping were examined in a broad doping and temperature range. At low temperature and low doping an enhancement of the power factor was obtained for compressive and tensile strain in the electron-doped case and for compressive strain in the hole-doped case. For the thermoelectrically more important high-temperature and high-doping regime a slight enhancement of the power factor was only found under small compressive strain with the power factor overall being robust against applied strain. To extend our findings the anisotropic thermoelectric transport of a [111]-oriented Si/Ge superlattice was investigated. Here, the cross-plane power factor under hole doping was drastically suppressed due to quantum-well effects, while under electron doping an enhanced power factor was found. For this, we state figures of merit of ZT = 0.2 and 1.4 at T = 300 and 900 K for the electron-doped [111]-oriented Si/Ge superlattice. All results are discussed in terms of band structure features.