  Post-selection strategies have been proposed with the aim of amplifying weak
signals, which may help to overcome detection thresholds associated with
technical noise in high-precision measurements. Here we use an optical setup to
experimentally explore two different post-selection protocols for the
estimation of a small parameter: a weak-value amplification procedure and an
alternative method, that does not provide amplification, but nonetheless is
shown to be more robust for the sake of parameter estimation. Each technique
leads approximately to the saturation of quantum limits for the estimation
precision, expressed by the Cram\'er-Rao bound. For both situations, we show
that information on the parameter is obtained jointly from the measuring device
and the post-selection statistics.
