Using LTspice's new arbitrary inductor, a simple linear inductor may
be modeled as Phi=L*i or in LTspice terminology:

Flux = {L}*x ; (no saturation)
Note: L is the parametrized inductance and x is the current through L.

Simple hard saturation can be modeled with a limit function:

Flux = {L}*limit(x,{-Is},{Is}) ; (hard saturation)
Note: Is is the parametrized saturation current.

A residual saturated inductance can easily be added to the model:

Flux = {L-Ls}*limit(x,{-Is},{Is})+{Ls}*x ; (stepped saturation)
Note: Ls is the parametrized saturation inductance.

The soft limit of the hyperbolic tangent can add more realism:

Flux ={(L-Ls)*Is}*tanh(x/{Is})+{Ls}*x ; (soft saturation)

For a very soft characteristic, use the arc tangent function:

Flux = {L*Is*2/Pi}*atan(x/{Is*2/Pi}) ; (very soft saturation)
Note: Ls is not really needed due to the very soft nature of atan.

A circuit file, saturating_inductor.asc, demonstrating these
techniques and more may be found in the files section of this Yahoo
Group under "adventures with analog". This file explores LTspice's
new arbitrary inductor model and compares it to other methods of
modeling inductor saturation, such as the B-source inductance
multiplier method, the generalized impedance converter method, and
a method with current controlled switches. -- analogspiceman