  We present JWST/NIRCam F187N, F200W, F405N and F410M direct imaging data of
the disk surrounding SAO 206462. Previous images show a very structured disk,
with a pair of spiral arms thought to be launched by one or more external
perturbers. The spiral features are visible in three of the four filters, with
the non-detection in F410M due to the large detector saturation radius. We
detect with a signal-to-noise ratio of 4.4 a companion candidate (CC1) that, if
on a coplanar circular orbit, would orbit SAO 206462 at a separation of
$\sim300$ au, $2.25\sigma$ away from the predicted separation for the driver of
the eastern spiral. According to the BEX models, CC1 has a mass of
$M_\mathrm{CC1}=0.8\pm0.3~M_\mathrm{J}$. No other companion candidates were
detected. At the location predicted by simulations of both spirals generated by
a single massive companion, the NIRCam data exclude objects more massive than
$\sim2.2~M_\mathrm{J}$ assuming the BEX evolutionary models. In terms of
temperatures, the data are sensitive to objects with
$T_{\text{eff}}\sim650-850$ K, when assuming planets emit like blackbodies
($R_\mathrm{p}$ between 1 and $3 R_\mathrm{J}$). From these results, we
conclude that if the spirals are driven by gas giants, these must be either
cold or embedded in circumplanetary material. In addition, the NIRCam data
provide tight constraints on ongoing accretion processes. In the low extinction
scenario we are sensitive to mass accretion rates of the order
$\dot{M}\sim10^{-9} M_\mathrm{J}$ yr$^{-1}$. Thanks to the longer wavelengths
used to search for emission lines, we reach unprecedented sensitivities to
processes with $\dot{M}\sim10^{-7} M_\mathrm{J}$ yr$^{-1}$ even towards highly
extincted environments ($A_\mathrm{V}\approx50$~mag).
