Gary and all,
Part of the problem (with NST's at least) may be due to the internal
current limiting shunts which reduce the effective coupling coefficient.
This will cause the measured voltage ratio to be somewhat different than
the actual turns ratio.
A more accurate approach might be to drive the LV side from a small
variac and then monitor the secondary voltage using the HV setting on a
DVM or a cheap analog meter. Or, use a simple resistive or capacitive HV
divider and a high-input impedance DVM. Driving the LV side at 10% of
its normal operating voltage should provide sufficient MMF to make the
core happy, while reducing the output to a lower, and safer, level.