  We present a simple method for the extraction of corrections for bias in the
measurement of the momentum of muons in hadron collider experiments. Such bias
can originate from a variety of sources such as detector misalignment, software
reconstruction bias, and uncertainties in the magnetic field. The two step
method uses the mean $<1/p^\mu_T>$ for muons from $Z\to \mu\mu$ decays to
determine the momentum scale corrections in bins of charge, $\eta$ and $\phi$.
In the second step, the corrections are tuned by using the average invariant
mass $<M^Z_{\mu\mu}>$ of $Z\to \mu\mu$ events in the same bins of charge $\eta$
and $\phi$. The forward-backward asymmetry of $Z/\gamma^{*} \to \mu\mu$ pairs
as a function of $\mu^+\mu^-$ mass, and the $\phi$ distribution of $Z$ bosons
in the Collins-Soper frame are used to ascertain that the corrections remove
the bias in the momentum measurements for positive versus negatively charged
muons. By taking the sum and difference of the momentum scale corrections for
positive and negative muons, we isolate additive corrections to $1/p^\mu_T$
that may originate from misalignments and multiplicative corrections that may
originate from mis-modeling of the magnetic field $(\int \vec{B} \cdot
d\vec{L})$. This method has recently been used in the CDF experiment at
Fermilab and in the CMS experiment at the Large Hadron Collider at CERN
