Does butter have any nutritional value or health benefits? That's debatable, but what is not debatable is whether a typical serving of butter has high antioxidant power... it definitely doesn't! Especially considering the fact that 100 grams of butter (the amount used in testing) equates to a staggering 717 calories, representing 255% of your daily allowance of saturated fat and 71% of cholesterol.
The testing of butter's ORAC value was done in Norway, using the the product "Tine" which is a popular brand of butter in the country. Although testing has not been done on U.S. sourced butter, one can presume its amount of antioxidants would at best be equal to Tine, but possibly be less than Tine. Why? Because when it comes to meat and dairy products, in the U.S. we pasteurize and perform other processes which aren't as prevalent in other countries. Heat and other production methods destroy most forms of antioxidants.
Research Support, Non-U.S. Gov't: Carlsen MH, Halvorsen BL, Holte K, et al. Nutrition Journal NIH Jan 2010