  We report on very-high-energy ($>$100 GeV) gamma-ray observations of Swift
J164449.3+573451, an unusual transient object first detected by the {\it Swift}
Observatory and later detected by multiple radio, optical and X-ray
observatories. A total exposure of 28 hours was obtained on Swift
J164449.3+573451 with VERITAS during 2011 March 28 -- April 15. We do not
detect the source and place a differential upper limit on the emission at 500
GeV during these observations of $1.4 \times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$
(99% confidence level). We also present time-resolved upper limits and use a
flux limit averaged over the X-ray flaring period to constrain various emission
scenarios that can accommodate both the radio-through-X-ray emission detected
from the source and the lack of detection by VERITAS.
