  Electrometry is performed using Rydberg states to evaluate the quadratic
Stark shift of the $5s^2$ $^1\textrm{S}_0-5s5p$ $^3\textrm{P}_0$ clock
transition in strontium. By measuring the Stark shift of the highly excited
$5s75d\;^1\textrm{D}_2$ state using electromagnetically induced transparency,
we characterize the electric field with sufficient precision to provide tight
constraints on the systematic shift to the clock transition. Using the
theoretically derived, and experimentally verified, polarizability for this
Rydberg state we can measure the residual field with an uncertainty well below
$1 \textrm{V} \textrm{m}^{-1}$. This resolution allows us to constrain the
fractional frequency uncertainty of the quadratic Stark shift of the clock
transition to $2\times10^{-20}$.
