  We present continuum extrapolated results of charmonium and bottomonium
correlators in the vector channel at several temperatures below and above
$T_c$. The continuum extrapolation jointly performed with the interpolations to
have physical values of $J/\psi$ and $\Upsilon$ masses in the confined phase is
based on calculations on several large quenched isotropic lattices using
clover-improved Wilson valence fermions carrying different quark masses. The
extrapolated lattice correlators are confronted with perturbation theory
results incorporating resummed thermal effects around the threshold from pNRQCD
and vacuum asymptotics above the threshold. An additional transport peak is
modelled below the threshold allowing for an estimate of the diffusion
coefficients for charm and bottom quarks. We find that charmonium correlators
in the vector channel can be well reproduced by perturbative spectral functions
above $T_c$ where no resonance peaks for $J/\psi$ are needed at and above 1.1
$T_c$, while for bottomonium correlators a resonance peak for $\Upsilon$ is
still needed up to 1.5 $T_c$. By analyzing the transport contribution to the
correlators we find that the drag coefficient of a charm quark is larger than
that of a bottom quark.
