On two of the months, the witnesses would desecrate Shabbos to come to Bais Din to say they saw the new moon. These months were Nissan and Tishrei which were special. Similarly the messengers would not leave Bais Din in these months until they actually heard them say that today is Rosh Chodesh. In the times of the Bais Hamikdash, they desecrated Shabbos every month in order to bring the proper korbanos of Rosh Chodesh in the correct time.

Rosh Hashana 1:5

Whether or not the moon was seen clearly, they would desecrate Shabbos to come to Bais Din. R’ Yosee says if the moon was clear, they would not desecrate Shabbos as others closer, who did not have to desecrate Shabbos, could come.