There are various ways to judge a response to a campaign these may include:
Changes in number of calls to the call center.
Number of Call Center calls specifically enquiring about the product or promotion in the campaign in question;
Variation in number of website visits;
Number of visits and click throughs to the specific page for the product being promoted or subject of the campaign;
There are also various primary research techniques and tools that can be utilized to evaluate awareness, product/promotion recall "T.O.M." and purchase intent. However, the trick here, though would raise the costs, is to conduct two rounds of research one before the campaign and one after.
Finally, advertising and media agencies who manage your campaigns can provide campaign effectiveness and reach matrices and reports that should help you though not conclusive.