  We derive an upper limit of 3 mJy (95% confidence) for the flux density at
317 MHz of the Geminga pulsar (J0633+1746). Our results are based on 7 hours of
fast-sampled VLA data, which we averaged synchronously with the pulse period
using a period model based on CGRO/EGRET gamma-ray data. Our limit accounts for
the fact that this pulsar is most likely subject to interstellar scintillations
on a timescale much shorter than our observing span. Our Bayesian method is
quite general and can be applied to calculate the fluxes of other scintillated
sources. We also present a Bayesian technique for calculating the flux in a
pulsed signal of unknown width and phase.
  Comparing our upper limit of 3 mJy with the quoted flux density of Geminga at
102 MHz, we calculate a lower limit to its spectral index of 2.7. We discuss
some possible reasons for Geminga's weakness at radio wavelengths, and the
likelihood that many of the unidentified EGRET sources are also radio-quiet or
radio-weak Geminga-like pulsars.
