Have you tried wget?
This cron job is what I use to update a news site each hour:
To get it to execute every 30 minutes:
0 * * * * nice wget -q -O /dev/null "http://www.yoursite.com/path/to/webcalendar/send_reminders.php
If "send_reminders.php" has includes, you may have to build a short php script with the includes and call "send_reminders.php" in that script. Then you would set the cron job to call your new script.
00 * * * * nice wget -q -O /dev/null "http://www.yoursite.com/path/to/webcalendar/send_reminders.php
30 * * * * nice wget -q -O /dev/null "http://www.yoursite.com/path/to/webcalendar/send_reminders.php