We report multifrequency observations with the NRAO Very Long Baseline Array ( VLBA ) of the compact radio sources J0128+6306 and J0547+2721 , which are viewed through the supernova remnants G127.1+0.5 and S147 , respectively . Observations were made at frequencies of 1.427 , 1.667 , 2.271 , and 4.987 GHz . The lines of sight to these sources pass through the shock wave and upstream and downstream turbulent layers of their respective supernova remnants , and thus might detect cosmic-ray generated turbulence produced during the Fermi acceleration process . For both sources , we detect interstellar scattering , characterized by a component of the angular size which scales as the square of the observing wavelength . The magnitude of the scattering is characterized by an effective scattering angular size \theta _ { S 0 } at a frequency of 1 GHz of 13.2 \pm 2.6 milliarcseconds ( mas ) for J0128+6306 and 6.7 \pm 2.2 mas for J0547+2721 . These angular sizes are consistent with the “ incidental ” scattering for any line of sight out of the galaxy at similar galactic latitudes and longitudes . There is therefore no evidence for enhanced turbulence at these supernova remnants . We establish upper limits to the supernova remnant-associated scattering measures of 8.1 - 14.8 m ^ { -20 / 3 } -pc for J0128+6306 and 3.0 m ^ { -20 / 3 } -pc for J0547+2721 .