We present the results of a spectroscopic survey to characterize chromospheric activity , as measured by \mathrm { H } \alpha emission , in low-mass members of the 500-Myr-old open cluster M37 . Combining our new measurements of \mathrm { H } \alpha luminosities ( L _ { \mathrm { H } \alpha } ) with previously cataloged stellar properties , we identify saturated and unsaturated regimes in the dependence of the L _ { \mathrm { H } \alpha } -to-bolometric-luminosity ratio , L _ { \mathrm { H } \alpha } / L _ { \mathrm { bol } } , on the Rossby number R _ { o } . All rotators with R _ { o } smaller than 0.03 \pm 0.01 converge to an activity level of L _ { \mathrm { H } \alpha } / L _ { \mathrm { bol } } = ( 1.27 \pm 0.02 ) \times 10 ^ { -4 } . This saturation threshold ( R _ { o, \mathrm { sat } } = 0.03 \pm 0.01 ) is statistically smaller than that found in most studies of the rotation-activity relation . In the unsaturated regime , slower rotators have lower levels of chromospheric activity , with L _ { \mathrm { H } \alpha } / L _ { \mathrm { bol } } ( R _ { o } ) following a power-law of index \beta = -0.51 \pm 0.02 , slightly shallower than the one found for a combined \approx 650-Myr-old sample of Hyades and Praesepe stars . By comparing this unsaturated behavior to that previously found for coronal activity in M37 ( as measured via the X-ray luminosity , L _ { \mathrm { X } } ) , we confirm that chromospheric activity decays at a much slower rate than coronal activity with increasing R _ { o } . While a comparison of L _ { \mathrm { H } \alpha } and L _ { \mathrm { X } } for M37 members with measurements of both reveals a nearly 1:1 relation , removing the mass-dependencies by comparing instead L _ { \mathrm { H } \alpha } / L _ { \mathrm { bol } } and L _ { \mathrm { X } } / L _ { \mathrm { bol } } does not provide clear evidence for such a relation . Finally , we find that R _ { o, \mathrm { sat } } is smaller for our chromospheric than for our coronal indicator of activity ( R _ { o, \mathrm { sat } } = 0.03 \pm 0.01 versus 0.09 \pm 0.01 ) . We interpret this as possible evidence for coronal stripping .