Tillman was supposed to throw a bullpen session on Saturday, but the Orioles are going wait another day or two on that, according to manager Buck Showalter.
The right-hander's been taking anti-inflammatory medicine to treat his arm, and the team wants to make sure the medicine is getting the chance to work all the way.
"He's played short and long toss, and both have been fine," Showalter said before Saturday's game. "I don't think Tilly's real happy about [being pushed back]."
Tillman came out of his last start, which came last Sunday in New York, due to elbow troubles. He then had an MRI done which showed the elbow's fine, but there's some inflammation with a nerve that's causing trouble.
There's still no official timetable on when Tillman might start pitching again or return to the rotation. The Orioles have not listed any starters past Sunday's series finale with the Yankees, where Zach Britton (5-1) is scheduled to go.