  Quadratic methods with heuristic weighting (e.g. pseudo-C_l or correlation
function methods) represent an efficient way to estimate power spectra of the
cosmic microwave background (CMB) anisotropies and their polarization. We
construct the sample covariance properties of such estimators for CMB
polarization, and develop semi-analytic techniques to approximate the
pseudo-C_l sample covariance matrices at high Legendre multipoles, taking
account of the geometric effects of mode coupling and the mixing between the
electric (E) and magnetic (B) polarization that arise for observations covering
only part of the sky. The E-B mixing ultimately limits the applicability of
heuristically-weighted quadratic methods to searches for the gravitational-wave
signal in the large-angle B-mode polarization, even for methods that can
recover (exactly) unbiased estimates of the B-mode power. We show that for
surveys covering one or two per cent of the sky, the contribution of E-mode
power to the covariance of the recovered B-mode power spectrum typically limits
the tensor-to-scalar ratio that can be probed with such methods to around 0.05.
