The same warnings that NeedMoreFans was under on May 21 applied to us (though somehow we didn't lose power). We had no shortage of squawks from our phones and weather radio throughout that evening, but I appreciated having local meteorologists add local context with the break-in coverage.
The station whose news/weather we watch most often mentioned before the storms hit (and reiterated on their social channels) that normal programming would be moved to their ".2" channel if they had to cut in. That was available over the air or via paid TV service. I thought it was reasonable.
One thing about severe weather response/coverage that I'd like to see better synced is when a warning polygon only covers part of a county. As OWBC states above, that's a big improvement on the NWS' part, but other parts of the all-around warning network are just not caught up to it. For example, if a tornado warning is issued for southeast Dane County for a storm moving east, that storm is not going to hit Madison - yet some weather alerts only acknowledge that "Dane County" is under a warning. I've been told to move library visitors to a storm shelter when the storm in question is in a different part of the county and moving away from Madison. I'll admit, though, that I don't know what it would take to improve that part.