  Quantum-enhanced measurements exploit quantum mechanical effects to provide
ultra-precise estimates of physical variables for use in advanced technologies,
such as frequency calibration of atomic clocks, gravitational waves detection,
and biosensing. Quantum metrology studies the fundamental limits in the
estimation precision given a certain amount of resources (e.g. the number of
probe systems) and restrictions (e.g. limited interaction time, or coping with
unavoidable presence of noise). Here we show that, even in the presence of
noise, probabilistic measurement strategies (which have a certain probability
of failure or abstention) can provide, upon a heralded successful outcome,
estimates with a precision that violates the deterministic bounds. This
establishes a new ultimate quantum metrology limit. For probe systems subject
to local dephasing, we quantify such precision limit as a function of the
probability of failure that can be tolerated. We show that the possibility of
abstaining can substantially set back the detrimental effects of noise.
