  We propose an estimation procedure for $d$-dimensional unitary
transformations. For $d>2$, the unitary transformations close to the identity
are estimated saturating the quantum Cram\'er-Rao bound. For $d=2$, the
estimation of all unitary transformations is also optimal with some prior
information. We show through numerical simulations that, even in the absence of
prior information, two-dimensional unitary transformations can be estimated
with greater precision than by means of standard quantum process tomography.
