  We address the following generic wave problem: is the estimation of the $N
\times N$ scattering matrix characterizing an arbitrarily complex linear system
with $N$ monomodal ports possible if waves can be input and output only via
$N_\mathrm{A}<N$ ports while the remaining $N_\mathrm{S}=N-N_\mathrm{A}$ ports
are terminated with tunable loads? We show that if $N_\mathrm{A}\geq 2$ and at
least three distinct and known tunable loads are available, the problem can be
solved (in closed form or via gradient descent) except for sign ambiguities on
the off-diagonal scattering coefficients involving the $N_\mathrm{S}$
not-directly-accessible (NDA) ports. Moreover, we demonstrate that a limitation
to phase-insensitive measurements only results in a mild additional blockwise
phase ambiguity. If the transmission from at least one accessible port to the
NDA ports can be measured, all ambiguities can be lifted. We corroborate our
results with microwave experiments on an 8-port chaotic cavity with
$N_\mathrm{A}=N_\mathrm{S}=4$. The demonstrated suite of techniques (coined
"virtual VNA") enables the characterization of an arbitrary linear $N$-port
system with an $N_\mathrm{A}$-port measurement device, where $N_\mathrm{A} \ll
N$. Potential applications include the contactless characterization of
miniaturized, embedded, receive-only and/or multi-element antenna systems and
programmable integrated photonic circuits, as well as wireless bioelectronic
sensing in complex media.
