A search for interstellar scintillation (ISS) of low-frequency variable radio sources is reported. Observations of 28 confirmed or suspected low-frequency variables, 21 nonvariable sources, and two pulsars were made at 408 MHz. As expected, the pulsars showed ISS, but scintillation was not detected in any other source. A typical upper limit to the rms modulation due to ISS is 150 mJy, giving lower limits to the apparent angular diameter of about 10 to the -6th arcsec. The possibilities that a true point source is broadened to an apparent angular diameter greater than or roughly equal to 10 to the -6th arcsec by scattering local to the source or in a general intergalactic medium are discussed.