After getting home from seeing the tree, I looked up juniper in both The Tree Identification Book by George Symonds, photographs by Stephen Chelminski, and in The Sibley Guide to Trees, written and illustrated by David Allen Sibley. Often I like the Sibley book the best, but in this case, I found that Symonds seemed to explain clearly how to tell the difference between red cedar (juniper), Atlantic white cedar, and northern white cedar. He says the red cedar has blue berry-like fruit, Atlantic white cedar fruit "is a ball-like cone," and northern white cedar (arborvitae) "has distinct cones." He also notes that red cedar may have some prickly needles, and the scale-like needles are four-sided, while Atlantic white cedar and northern white cedar have flatter needles. I have known since I was a kid that the juniper needles are less flat, but I didn't really know that they were four-sided.
Here are the blue, berry-like fruits of the juniper I saw today.
On the juniper page, the Symonds book also mentions a cedar gall or cedar apple, saying "It is orange in color and often develops in wet weather, drying up in dry weather. Maybe that's what this is:
In contrast, here are the cones and flat leaves of the northern white cedar:
