I was planning to spray Roundup on some blackberry roots/stems near newly-planted Excelsa cedars. If I spray, will the nearby trees be okay?
The active ingredient in Roundup is glyphosate. It works only on green leaf material. Minor overspray that gets on the foliage of your nearby trees may cause the sprayed area to turn brown, but it is not likely to overly impact the tree. That said, it's best to spray on a non-windy day. The hotter the day, the better.
For blackberries, I would wait until they emerge vigorously from the ground and then spray. Spraying dormant or low vigor sprigs will be less effective than spraying vigorous plants.
If you are looking for a non-chemical approach, you may consider simply digging out the new shoots. This is pretty easy to accomplish and the results are immediate.
Best of luck,