We present high contrast images of the hydrogen white dwarf G 29-38 taken in the near infrared with the Hubble Space Telescope and the Gemini North Telescope as part of a high contrast imaging search for substellar objects in orbit around nearby white dwarfs . We review the current limits on planetary companions for G29-38 , the only nearby white dwarf with an infrared excess due to a dust disk . We add our recent observations to these limits to produce extremely tight constraints on the types of possible companions that could be present . No objects > 6 M _ { Jup } are detected in our data at projected separations > 12 AU , and no objects > 16 M _ { Jup } are detected for separations from 3 to 12 AU , assuming a total system age of 1 Gyr . Limits for companions at separations < 3 AU come from a combination of 2MASS photometry and previous studies of G29-38 ’ s pulsations . Our imaging with Gemini can not confirm a tentative claim for the presence of a low mass brown dwarf . These observations demonstrate that a careful combination of several techniques can probe nearby white dwarfs for large planets and low mass brown dwarfs .