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The Milagro telescope monitors the northern sky for 100 GeV to 100 TeVtransient emission through continuous very high energy wide-field observations.The large effective area and ~100 GeV energy threshold of Milagro allow it todetect very high energy (VHE) gamma-ray burst emission with much highersensitivity than previous instruments and a fluence sensitivity at VHE energiescomparable to that of dedicated gamma-ray burst satellites at keV to MeVenergies. Even in the absence of a positive detection, VHE observations canplace important constraints on gamma-ray burst (GRB) progenitor and emissionmodels. We present limits on the VHE flux of 40 s -- 3 h duration transientsnearby to earth, as well as sensitivity distributions which have been correctedfor gamma-ray absorption by extragalactic background light and cosmologicaleffects. The sensitivity distributions suggest that the typical intrinsic VHEfluence of GRBs is similar or weaker than the keV -- MeV emission, and wedemonstrate how these sensitivity distributions may be used to placeobservational constraints on the absolute VHE luminosity of gamma-ray burstsfor any GRB emission and progenitor model.Comment: Accepted for publication in ApJL, minor revisions to the text,  retypeset in emulateapj styl

Limits on Very High Energy Emission from Gamma-Ray Bursts with the Milagro Observatory