Determination of Cell constant
Conductivity measurements were done in late 1800s by Friedrich Kohlrausch, who painstakingly measured the conductivities of solutions so accurately that they are still valid today. Most of his work is in German was published in relatively unknown journals. In his time, conductivity theory was not advanced enough to predict the conductivity of simple salt solutions in water, so there was no a priori theoretical prediction of conductivity, from the first principles. I don't think it is doable today after 100 years (may well be wrong(.
However, the accurate measurement of resistance was well established in physics. See below.
A paper in the J. Am. Chem. Soc. 1933, 55, 5, 1780 describes what Kohlrausch and his meticulous colleagues they did. Note the level of details which is remarkably missing from papers today.

After Kohlrausch had developed his method of measuring the electrical
conductance of solutions by means of an alternating current bridge, he
undertook with the aid of Holborn and Diesselhorst’ the determination
of the specific conductance of seven standard reference solutions in
absolute units in order that the results might be available to himself
and to other experimenters for the calibration of conductance cells.
For this purpose they used two cells whose cross sectional areas, a,
and length, l, were determined mechanically. The cell constant,
l/a, could then be computed in absolute units (cm$^{-1}$) from the measured dimensions.
The cell constants of a considerable number of other cells with
sealed-in electrodes of the usual type were determined electrically by
comparison with the primary cells by measurements of resistance when
filled with a common solution. These cells, whose cell constants were
thus determined indirectly, were then used for the determination of
the specific conductance of the seven standard reference solutions at
approximately 0, 9, 18, 27 and 36 C. The specific conductance of each
of these solutions for every degree between 0 and 36 C was obtained by
interpolation. No actual measurements were made at either 20 or at
25’. The water-bath used to fix the temperature of the cells was not
provided with an automatic thermostatic control. The majority of the
data on conductance in the literature are based on the values ascribed
to these standard reference solutions by Kohlrausch, especially the 1
N and 0.1 N potassium chloride solutions.
In the original paper by Kohlrausch, Holborn and Diesselhorst it is
stated that the normal potassium chloride solution was prepared by
dissolving 74.555 g. of potassium chloride weighed in air and making
up to 1 liter at 18 C. The 0.1, 0.02, and 0.01 normal solutions were
prepared by dilution by volume. The book “Das Leitvermogen der
Elektrolyte” by Kohlrausch and Holborn, which was published in the
same year as the paper referred to, contains alternative directions
for the preparation of these solutions by weight. This book has
probably been used by other experimenters more than the original paper
because it is more generally available.