LTspice does have a capmeter: SpecialFunctions\capmeter, and capometer.sub that works in a .tran analysis, but I've yet to find good instructions for using it. I did however reverse engineer the subcircuit back to a node and component identical schematic, which may aid an expert in understanding it enough to explain its use.
N.B. pins 1 (DUT+) and 2 (DUT-) have no DC path to ground - you *MUST* provide them externally.
N.B.2. Its outputs 4 (Resistance) and 5 (Capacitance) are blanked for the first 10us of the sim and thereafter will require approx 10us to reach steady state. If you are sweeping bias, sweep it sloooooly!
The attachment is just the capometer internal schematic, its *NOT* a ready to run demo of its use.
Ian.M thank you for your reverse engineering efforts.
There are some controls in the Capometer.
If you [CTRL RIGHT-CLICK] on the model you get:

These are let you set the following:
current = 1m <- this is the amplitude of the small signal test current
freq = 3MEG <- this is the frequency of the small signal test current.
C=0.5u <- not 100% certain, but this may be a blocking capacitor in series with the DUT.
Q=0.25 <- haven't figured this out.
The primary use of this tool was for checking to see how semiconductor parameters, for example, Coss in MOSFET, varies with DC bias.
This thread is inspiring me to make an inductor meter for checking inductance versus DC bias current.
Regards,
Jay_Diddy_B