The swimming season on the Montenegro coast runs from around mid-June to late September, with the sea warm enough for comfortable swimming throughout those months.
July and August are the peak months — sea temperatures reach roughly 25–26°C in August, the beaches are at their busiest, and most beach bars and clubs are fully operational. June and September are the shoulder months: water is still warm and pleasant, crowds are noticeably thinner, and prices tend to be lower.
If you're sensitive to cold water, aim for late July through August. If you prefer a quieter experience without sacrificing good swimming conditions, early June or the first half of September are excellent windows.