We report on very high energy (E > 100 GeV) gamma-ray observations of V407 Cygni, a symbiotic binary that underwent a nova outburst producing 0.1-10 GeV gamma rays during 2010 March 10-26. Observations were made with the Very Energetic Radiation Imaging Telescope Array System during 2010 March 19-26 at relatively large zenith angles due to the position of V407 Cyg. An improved reconstruction technique for large zenith angle observations is presented and used to analyze the data. We do not detect V407 Cygni and place a differential upper limit on the flux at 1.6 TeV of 2.3 × 10–12 erg cm–2 s–1 (at the 95% confidence level). When considered jointly with data from Fermi-LAT, this result places limits on the acceleration of very high energy particles in the nova.