  The impact of theoretical and experimental uncertainties on the indirect
determination of the Higgs boson mass, MH, in the Standard Model (SM) is
discussed. Special emphasis is put on the electroweak precision observables MW
(the W boson mass) and sin^2(theta_eff) (the effective leptonic mixing angle).
The current uncertainties of the theoretical predictions for MW and
sin^2(theta_eff) due to missing higher order corrections are conservatively
estimated to delta MW \approx 7 MeV and delta sin^2(theta_eff) \approx 7 x
10^-5 . Expectations and necessary theoretical improvements for future
colliders are explored. Results for the indirect MH determination are presented
based on the present experimental and theoretical precisions as well as on
improvements corresponding to the prospective situation at future colliders.
The treatment of the different future colliders is done in a uniform way in
order to allow for a direct comparison of the accuracies that can be reached.
Taking all experimental, theoretical, and parametric uncertainties into
account, a current upper bound on MH of \sim 200 GeV is obtained. Furthermore
we find in a conservative approach that a Linear Collider with GigaZ
capabilities can achieve a relative precision of about 8% (or better) in the
indirect determination of MH.
