Moto's shipping notifications, etc. are a bit overloaded. I ordered my Moto 360 (silver) on the 16th (estimated arrival was supposed to be today, the 24th). I did an online chat with Motorola support yesterday around 6pm and found out they had shipped it just 3 hours prior to the chat session. He gave me my tracking number. With two business day shipping, it's going to be a day late, but at least it's coming.
I didn't get the notification email from Motorola (nor did they update the order status on their site) that it had shipped until about 8 hours later.
All I can say is try to be patient and if your estimated ship date comes and goes, hit them up on the chat support. They should at least be able to tell you what's going on.
I should also note, they charged my credit card the day of my order, even though they weren't going to ship my watch until more than a week later. When I first saw that they had charged my card I figured that the estimated delivery date was an "under-promise and over-deliver" estimate, because most companies don't charge you until they actually ship. When I kept checking the site and seeing that they hadn't shipped, I got worried and hit them up on the chat. I also emailed them, but my email went unanswered. So, again, all I can suggest is to try to be patient and just follow up if estimated dates elapse.