Abstract Modifications of the matter power spectrum due to baryonic physics are one of the major theoretical uncertainties in cosmological weak lensing measurements. Developing robust mitigation schemes for this source of systematic uncertainty increases the robustness of cosmological constraints, and may increase their precision if they enable the use of information from smaller scales. Here we explore the performance of two mitigation schemes for baryonic effects in weak lensing cosmic shear: the principal component analysis (PCA) method and the halo-model approach in hmcode. We construct mock tomographic shear power spectra from four hydrodynamical simulations, and run simulated likelihood analyses with cosmolike assuming LSST-like survey statistics. With an angular scale cut of ℓmax < 2000, both methods successfully remove the biases in cosmological parameters due to the various baryonic physics scenarios, with the PCA method causing less degradation in the parameter constraints than hmcode. For a more aggressive ℓmax = 5000, the PCA method performs well for all but one baryonic physics scenario, requiring additional training simulations to account for the extreme baryonic physics scenario of Illustris; hmcode exhibits tensions in the 2D posterior distributions of cosmological parameters due to lack of freedom in describing the power spectrum for $k \gt 10\ h^{-1}\, \mathrm{Mpc}$. We investigate variants of the PCA method and improve the bias mitigation through PCA by accounting for the noise properties in the data via Cholesky decomposition of the covariance matrix. Our improved PCA method allows us to retain more statistical constraining power while effectively mitigating baryonic uncertainties even for a broad range of baryonic physics scenarios.