Greetings Walter,
Tree age is determine via three primary methods: (1) cutting down the tree and counting the tree rings on the stump; (2) using an increment borer to extract a core in which you then can count tree rings; or knowing the date of tree/forest establishment.
If you want to keep your tree standing, then option one is not very practical. Option two causes minimal tree damage but is not really recommended for urban or yard trees. Option three is the most realistic option for most yard trees seeing that many owners have an idea when the home was built.
The Illinois Big Tree Register http://web.extension.uiuc.edu/forestry/il_big_tree.html is our champion tree program. Guidelines for big tree "qualification" are found on the aforementioned Website. Unfortunately, non-native species and cultivars are not eligible for the Illinois Big Tree Register.
