  We introduce a two-channel tunneling model to generalize the widely used BTK
theory of point-contact conductance between a normal metal contact and
superconductor. Tunneling of electrons can occur via localized surface states
or directly, resulting in a Fano resonance in the differential conductance
$G=dI/dV$. We present an analysis of $G$ within the two-channel model when
applied to soft point-contacts between normal metallic silver particles and
prototypical heavy-fermion superconductors CeCoIn$_5$ and CeRhIn$_5$ at high
pressures. In the normal state the Fano line shape of the measured $G$ is well
described by a model with two tunneling channels and a large
temperature-independent background conductance. In the superconducting state a
strongly suppressed Andreev reflection signal is explained by the presence of
the background conductance. We report Andreev signal in CeCoIn$_5$ consistent
with standard $d_{x^2-y^2}$-wave pairing, assuming an equal mixture of
tunneling into [100] and [110] crystallographic interfaces. Whereas in
CeRhIn$_5$ at 1.8 and 2.0 GPa the signal is described by a $d_{x^2-y^2}$-wave
gap with reduced nodal region, i.e., increased slope of the gap opening on the
Fermi surface. A possibility is that the shape of the high-pressure Andreev
signal is affected by the proximity of a line of quantum critical points that
extends from 1.75 to 2.3 GPa, which is not accounted for in our description of
the heavy-fermion superconductor.
