The world number 53 said: "I'm sure I'll play Sloane a lot in the future. I'm sure after today she's going to be top 20. So good for her."
Stephens, who is just 10 months older than Robson, has known the Brit since they were 12.
This was the pair's second meeting this month, having faced each other in the first round of the Hobart International less than a fortnight ago.