Radio-frequency (rf) electrical sources are commonly used to generate plasmas for processing of industrial materials and for related experimental work. Published descriptions of such plasmas usually include generator-power measurements, and occasionally include plasma dc-bias measurements. One or both of these quantities are also used in industrial feedback control systems for setpoint regulation. Recent work at Sandia and elsewhere with an experimental rf discharge device (the "GEC RF Reference Cell") has shown that power and dc-bias levels are often insufficient information for specifying the state of the plasma. The plasma can have nonlinear electrical characteristics that cause harmonic generation, and the harmonic levels can depend sensitively on the impedance of the external circuitry at harmonic frequencies. Even though the harmonics may be low in amplitude, they can be directly related to large changes in plasma power and to changes in optical emission from the plasma. Consequently, in order for a worker to truly master the plasma-generation process, it is necessary to understand, measure, and control electrical characteristics of the plasma. In this paper we describe techniques that have been developed from work with the Reference Cell for making electrical measurements on rf plasmas, and we describe surprising observations of harmonic behavior.