  A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to
be continuously embedded into $L^\infty(\mathbb R^n)$ is exhibited. Under the
same assumption, any function from the relevant fractional-order spaces is
shown to be continuous. Improvements of this result are also offered. They
provide the optimal Orlicz target space, and the optimal
rearrangement-invariant target space in the embedding in question. These
results complement those already available in the subcritical case, where the
embedding into $L^\infty(\mathbb R^n)$ fails. They also augment a classical
embedding theorem for standard fractional Sobolev spaces.
