How about in the List & Search >> Search Form >> add the calendar field to the "Hidden" section ... press button #3 (Match + Stage) and in the "Match" column select the appropriate setting from the "Date & Time" group, e.g. "Future (> or =)"
Thank you for the idea, for this solution i will need default calendar date to be today date. Did you have any idea how to set default today date in calendar field on search form ?