inductorltspiceparalleltransformervoltage-source
This is a circuit I designed in LT Spice. There is no transformer component in LT Spice so I specified L1 and L2 as magnetically coupled with K L1 L2 1 when I try to simulate I get an error that I have to add series resistance in order to run the simulation…
How do I avoid adding a useless resistor?
In LTSpice, every node needs a path to GND. Just tack a GND node to both your primary and secondary side (drawn in CircuitLab for simplicity):
simulate this circuit – Schematic created using CircuitLab
Transformers are darned hard to model for many reasons:
As you have stated, core materials do not have a linear permeability, but vary as they become saturated and also vary with transformer temperature. If you look at a standard BH curve like the one below you will see the issues. Each time you magnetize the core in one direction, it retains some magnetism and when you reverse current, energy is required to first demagnetize and then re-magnetize in the opposite direction (called hysteresis). Since the apparent inductance is related to the slope of the curve, it is dependent on not only on what the instantaneous voltage and di/dt are but what path you took to get there. Add to this the troubling fact that any DC component of your signal pushes you up or down the curve to a place where the slope of the line is different. Throw in the resistance of the coils and the capacitance of the wires lying next to each other, and the fact that the hysteresis losses and eddy currents actually get hot and dissipate power (making them non-linear resistive components in your model), and you can understand why attempts at models all have loss factors and other "lumped" type parameters in them. I guess this is not really an answer, but it wouldn't fit as a comment. 
Best Answer
As The Photon points out, in anything realistic, there is a resistance (unless you are from the future and build everything with superconductors).
You try to put an ideal voltage source (btw. the ltspice setting is amplitude, and you probably want 120V rms) in parallel with an ideal inductor, both without any kind of resistance. What would probably be the current hat flows (and in turn, the voltage that comes out on the secondary)?
So infinite current is likely not wanted, thus any kind of resistance at that point is not at all useless. But maybe you were referring to a resistor component as being useless? Just right click the inductor (or better both of them) and set their series resistance value to something realistic (which depends on what kind of transformer you have in mind).