  Fragile quantum features such as entanglement are employed to improve the
precision of parameter estimation and as a consequence the quantum gain becomes
vulnerable to noise. As an established tool to subdue noise, quantum error
correction is unfortunately overprotective because the quantum enhancement can
still be achieved even if the states are irrecoverably affected, provided that
the quantum Fisher information, which sets the ultimate limit to the precision
of metrological schemes, is preserved and attained. Here, we develop a theory
of robust metrological schemes that preserve the quantum Fisher information
instead of the quantum states themselves against noise. After deriving a
minimal set of testable conditions on this kind of robustness, we construct a
family of $2t+1$ qubits metrological schemes being immune to $t$-qubit errors
after the signal sensing. In comparison at least five qubits are required for
correcting arbitrary 1-qubit errors in standard quantum error correction.
