We present the results of 71.6 hr of observations of the Geminga pulsar (PSR J0633+1746) with the VERITAS veryhigh-energy gamma-ray telescope array. Data taken with VERITAS between 2007 November and 2013 February were phase-folded using a Geminga pulsar timing solution derived from data recorded by the XMM-Newton and Fermi-LAT space telescopes. No significant pulsed emission above 100 GeV is observed, and we report upper limits at the 95% confidence level on the integral flux above 135 GeV (spectral analysis threshold) of 4.0 × 10 −13 s −1 cm −2 and 1.7 × 10 −13 s −1 cm −2 for the two principal peaks in the emission profile. These upper limits, placed in context with phase-resolved spectral energy distributions determined from 5 yr of data from the Fermi-Large Area Telescope (LAT), constrain possible hardening of the Geminga pulsar emission spectra above ∼50 GeV.