The proposed European Space Agency (ESA) BIOMASS satellite will comprise a P-band (435 MHz) polarimetric synthetic aperture radar (SAR). Its primary objective is to determine forest biomass density by correlation with the backscatter intensity and covariances of SAR images measured in four polarization channels - HH, HV, VH, and VV - together with height measurements from polarimetric interferometry. Faraday rotation (FR) in the ionosphere alters the balance in the polarimetric channels, thus affecting the accuracy of derived biomass density measurements. The accuracy of five techniques for estimating FR from polarimetric SAR images has been assessed using simulated images of boreal forest with a range of biomass densities, FR angles and system errors. The latter include H/V channel imbalances, antenna cross-talk and noise. FR estimation errors due to channel imbalances up to 0.1 dB are found to be negligible but all methods have biases dependent on the FR and the relative phases of the cross-talk components. However, the best-performing estimator corrects to better than 4° under worst-case system errors, so the accuracy of biomass density estimates will not be significantly affected. Under conditions of low signal-to-noise, the FR estimate must employ maximum likelihood averaging to prevent an unacceptable bias towards the independent FR estimate, which is used to resolve a π/2 angle ambiguity. Further simulations illustrate correction performance for structured images (from an L-band satellite SAR) and the application of large sinusoidal FR perturbations in the image (simulating non-uniform ionospheric perturbations).