Neutral molecules, isolated in the gas-phase, can be prepared in a long-lived excited state and stored in a trap. The long observation time afforded by the trap can then be exploited to measure the radiative lifetime of this state by monitoring the temporal decay of the population in the trap. This method is demonstrated here and used to benchmark the Einstein $A$-coefficients in the Meinel system of OH. A pulsed beam of vibrationally excited OH radicals is Stark decelerated and loaded into an electrostatic quadrupole trap. The radiative lifetime of the upper $Lambda$-doublet component of the $X ^2Pi_{3/2}, v=1, J=3/2$ level is determined as $59.0 pm 2.0$ ms, in good agreement with the calculated value of $57.7 pm 1.0$ ms.