I recommend the Widget Options plugin.
Install that plugin and then add a widget to the ‘Page Sidebar’ and control which pages it appears on with the extra settings that the plugin adds to the widget.
For example, make a note of the page ID of your contact page and add is_single( '27' ) (change ’27’ for your actual page ID) in the ‘Logic’ tab of the Widget Options settings.
The conditional tag is_single( '27' ) will only show the widget on the page with the ID of 27.
See the image below where I have marked the location of the ‘Logic’ tab with the green arrows.
