  If $\gamma$-ray bursts (GRBs) are accompanied by gravitational wave bursts
(GWBs) the correlated output of two gravitational wave detectors evaluated in
the moments just prior to a GRB will differ from that evaluated at times not
associated with a GRB. We can test for this difference independently of any
model of the GWB signal waveform. If we invoke a model for the GRB source
population and GWB radiation spectral density we can find a confidence interval
or upper limit on the root-mean-square GWB signal amplitude in the detector
waveband. To illustrate we adopt a simple, physically motivated model and
estimate that initial LIGO detector observations coincident with 1000 GRBs
could lead us to exclude, with 95% confidence, associated GWBs with $h_{RMS}
\gtrsim 1.7 \times 10^{-22}$. This result does not require the detector noise
be Gaussian or that any inter-detector correlated noise be measured or
measurable; it does not require advanced or a priori knowledge of the source
waveform; and the limits obtained on the wave-strength improve with the number
of observed GRBs.
