Thank you, John, Leigh, and Joel for your insights. John, especially,
pointed out the pitfalls associated with the concept of "DC
capacitance" or "zero-frequency capacitance". In retrospect, what I
meant was to ask about the measurement of capacitance at very low
frequency (case (1) of John's response), hoping to avoid (at least
until optics, where a connection is made between dielectric constant
and index of refraction) the complications that arise in connection
with dielectrics at much higher frequencies. Another unstated
assumption was that I was trying to avoid the use of digital LCR
meters, which would make things far too easy for the students.
Given the idea of bridge circuits, I found a couple of sites that
discuss them; the latter site is actually an online lab manual for an
EE course.