We report on Raman scattering and optical emission spectroscopy (OES) measurements in recombining atmospheric pressure plasmas of air and nitrogen. An inductively coupled plasma torch is used to create an equilibrium plasma, which is then forced to rapidly recombine by flowing through a water-cooled tube. For all conditions, temperature measurements are performed using OES and Raman scattering at the exit of tubes of varying lengths. The density of atomic nitrogen is also determined. Evidence of strong chemical nonequilibrium is found in a number of cases. For these cases, we observe that the rotational temperatures measured with OES differ from those measured with Raman scattering, and that the atomic nitrogen density is elevated with respect to equilibrium. A power balance analysis confirms that a large fraction of gas enthalpy is stored in the non-recombined nitrogen atoms. For cases where the plasma remains in equilibrium, we perform numerical simulations using the Eilmer3 computational fluid dynamics (CFD) code. Eilmer3 does not predict the observed drop in gas temperature measured using Raman scattering and OES. Prior efforts by the CFD community have also failed to correctly predict this temperature drop. The results presented in this paper are therefore intended as validation test cases for CFD simulations.