  Low-mass (< 1.2 Solar mass) main-sequence stars lose angular momentum over
time, leading to a decrease in their magnetic activity. The details of this
rotation-activity relation remain poorly understood. Using observations of
members of the $\approx$700 Myr-old Praesepe and Hyades open clusters, we aim
to characterize the rotation-activity relation for different tracers of
activity at this age. To complement published data, we obtained new optical
spectra for 250 Praesepe stars, new X-ray detections for ten, and new rotation
periods for 28. These numbers for Hyads are 131, 23, and 137, respectively. The
latter increases the number of Hyads with periods by 50%. We used these data to
measure the fractional H$\alpha$ and X-ray luminosities,
$\mathit{L}_{H\alpha}/\mathit{L}_{bol}$ and $\mathit{L}_X/\mathit{L}_{bol}$,
and to calculate Rossby numbers $\mathit{R}_o$. We found that at $\approx$700
Myr almost all M dwarfs exhibit H$\alpha$ emission, with binaries having the
same overall color-H$\alpha$ equivalent width distribution as single stars. In
the $\mathit{R}_o-\mathit{L}_{H\alpha}/\mathit{L}_{bol}$ plane, unsaturated
single stars follow a power-law with index $\beta = -5.9 \pm 0.8$ for
$\mathit{R}_o > 0.3$. In the $\mathit{R}_o-\mathit{L}_X/\mathit{L}_{bol}$
plane, we see evidence for supersaturation for single stars with $\mathit{R}_o
\lesssim 0.01$, following a power-law with index $\beta_{sup} =
0.5^{+0.2}_{-0.1}$, supporting the hypothesis that stellar coronae are being
centrifugally stripped. We found that the critical $\mathit{R}_o$ value at
which activity saturates is smaller for $\mathit{L}_X/\mathit{L}_{bol}$ than
for $\mathit{L}_{H\alpha}/\mathit{L}_{bol}$. Finally, we observed an almost 1:1
relation between $\mathit{L}_{H\alpha}/\mathit{L}_{bol}$ and
$\mathit{L}_X/\mathit{L}_{bol}$, suggesting that both the corona and the
chromosphere experience similar magnetic heating.
