  One way to uniquely define Schramm-Loewner Evolution (SLE) in multiply
connected domains is to use the restriction property. This gives an implicit
definition of a $\sigma$-finite measure on curves; yet it is in general not
clear how to construct such measures nor whether the mass of these measures,
called the partition function, is finite.
  We provide an explicit construction of the such conformal restriction SLEs in
multiply connected domains when $\kappa = 4$ using the Gaussian Free Field
(GFF). In particular, both when the target points of the curve are on the same
or on distinct boundary components, we show that there is a mixture of laws of
level lines of GFFs that satisfies the restriction property. This allows us to
give an expression for the partition function of $\mathrm{sle}_4$ on multiply
connected domains and shows that the partition function is finite, answering
the question raised in [Lawler, J. Stat. Phys. 2009].
  In a second part, we provide a second construction of $\mathrm{sle}_\kappa$
in multiply-connected domains for the whole range $\kappa \in (8/3,4]$;
specific, however, to the case of the two target points belonging to the same
boundary components. This is inspired by [Werner, Wu, Electron. J. Probab.
2013] and consists of a mixture of laws on curves obtained by following
$\mathrm{cle}_\kappa$ loops and restriction hulls attached to parts of the
boundary of the domain. In this case as well, we obtain as a corollary the
finiteness of the partition function for this type of $\mathrm{sle}_\kappa$.
