Still, please resist the self-focused text:
"On my way",
as this tells us very little - where are you, how long will it take, and more - this is not giving us a lot of information!
That text serves as a gesture, and not an update.
And, replace it with:
"ETA of 1:03 PM",
since this shares that you are running behind (do apologize for that), and when your friend/colleague can expect you.
With a focus on the other person making the most of his time and not simply waiting for you, that will show respect and allow for planning for that time frame!