In NJ you get a choice of which EzPass transponder (the white thing) you get. Either the windshield mount or the license plate mount.
The windshield mount comes with clear, 3M-backed sticky/plastic "velcro", but a lot of people buy the plastic mount with suction cups (found at most car washes for $5)
I keep mine in the glovebox until needed. (i have never heard of being ticketed for holding it up to the windshield)
Side note: I also drive a motorcycle, and generally hold it in my hand as I coast through, although sometimes i'll go with the windshield suction mount.
Want the license plate mount? report your transponder lost, then request the license plate mount.