We study gravitational wave production from gauge preheating in a variety of inflationary models, detailing its dependence on both the energy scale and the shape of the potential. We show that preheating into Abelian gauge fields generically leads to a large gravitational wave background that contributes significantly to the effective number of relativistic degrees of freedom in the early universe,
N
eff
. We demonstrate that the efficiency of gravitational wave production is correlated with the tensor-to-scalar ratio,
r
. In particular, we show that efficient gauge preheating in models whose tensor-to-scalar ratio would be detected by next-generation cosmic microwave background experiments (
r
≳
1
0
−
3
) will be either detected through its contribution to
N
eff
or ruled out. Furthermore, we show that bounds on
N
eff
provide the most sensitive probe of the possible axial coupling of the inflaton to gauge fields regardless of the potential.