Glib answer: nothing, since those letters were removed from the Montenegrin alphabet in 2017; they've been replaced with sj and zj, same as in Serbo-Croatian.
Actual answer: phonemically, they represent
/sj zj/ or
/ɕ ʑ/, depending on your analysis.
Most native speakers of Serbo-Croatian pronounce these phonemes (or clusters) as something like
[ɕj ʑj]: that is, the
[j] is clearly heard. And the sequences
[sj zj] don't appear. So the standard orthography writes these sounds as sj zj, taking the palatalization as allophonic before the palatal
In Montenegro, though, these phonemes/clusters are realized more like
[ɕ ʑ], with the off-glide disappearing. So analyzing them as phonemic, and using the special letters ś ź, is way of distinguishing the Montenegrin identity from wider Serbo-Croatian.
The letters never really caught on, though, nor did their companion з (for
[dz]). And their Cyrillic equivalents have no precombined codepoints in Unicode, which makes them difficult to use electronically. On top of that, it's been pointed out that many people in Montenegro still pronounce the off-glide, while people in e.g. Herzogovina don't.
So the government eventually made the decision to drop their custom letters entirely, and stick with the more traditional sj zj for all official purposes.