Several of this year’s praying mantises set up shop in the decorative grasses bracketing the front door:

We found their egg masses, formally called ootheca, attached to the stems in mid-October:

They feel like rigid urethane foam and seem eminently protective:

We’ll cut around the masses when it’s time to clear out the dead grass next spring. I was tempted to bring one inside, but dealing with a gazillion tiny mantises in a few months would be daunting.
They are very much like urethane foam. If they happen to reside on something that has to be cut down at the end of the season, I rescue them and place them in various safer locations. If you look at the obvious “seam” closely, you can see the difference from one that is old vs one that is still “loaded”. I’ve never actually found one in the process of creating an egg mass but I would suppose it takes a while and would be inserting to watch.