  We investigate the coupling factor $\phi_\mu$ that quantifies the magnetic
flux $\Phi$ per magnetic moment $\mu$ of a point-like magnetic dipole that
couples to a superconducting quantum interference device (SQUID). Representing
the dipole by a current-carrying loop, the reciprocity of mutual inductances of
SQUID and loop provides a way of calculating $\phi_\mu(\vec{r}, \vec{e}_\mu)$
vs.~position $\vec{r}$ and orientation $\vec{e}_\mu$ of the dipole anywhere in
space from the magnetic field $B(\vec{r})$ produced by a supercurrent
circulating in the SQUID loop. We use numerical simulations based on London and
Ginzburg-Landau theory to calculate $\phi_\mu$ from the supercurrent density
distributions in various SQUID geometries. We treat the far-field regime
($r\gtrsim a=$ inner size of the SQUID loop) with the dipole placed on the
symmetry axis of circular or square shaped loops. We compare expressions for
$\phi_\mu$ from filamentary loop models with simulation results for loops with
finite width $w$ (outer size $A>a$), thickness $d$ and London penetration depth
$\lambda_L$ and show that for thin ($d\ll a$) and narrow ($w < a$) loops the
introduction of an effective loop size $a_{\rm eff}$ in the filamentary
loop-model expressions results in agreement with simulations. For a dipole
placed in the center of the loop, simulations provide an expression
$\phi_\mu(a,A,d,\lambda_L)$ that covers a wide parameter range. In the
near-field regime (dipole centered at small distance $z$ above one SQUID arm)
only coupling to a single strip representing the SQUID arm has to be
considered. Here, we compare simulations with an analytical expression derived
for a homogeneous current density distribution, which yields excellent
agreement for $\lambda_L>w,d$. Moreover, we analyze $\phi_\mu$ provided by the
introduction of a constriction in the SQUID arm below the magnetic dipole.
