  In the context of multiparameter quantum estimation theory, we investigate
the construction of linear schemes in order to infer two classical parameters
that are encoded in the quadratures of two quantum coherent states. The
optimality of the scheme built on two phase-conjugate coherent states is proven
with the saturation of the quantum Cram\'er--Rao bound under some global energy
constraint. In a more general setting, we consider and analyze a variety of
$n$-mode schemes that can be used to encode $n$ classical parameters into $n$
quantum coherent states and then estimate all parameters optimally and
simultaneously.
