Chatwood, who is recovering from an impingement in his right elbow and has been on the 15-day disabled list since Aug. 8, indicated he is ready for a rehab assignment.
"Everything went well," Weiss said of Chatwood's session. "We're going to look to get him out on a rehab assignment sometime next week, so he's coming along."
Oswalt, who went on the DL after straining his left hamstring July 7, suffered a setback during a simulated game Aug. 10, but he also had a positive session Saturday.
"We're planning on him throwing a simulated game when we get back home," Weiss said of Oswalt. "He's a little bit behind Tyler, but he had a good day. His bullpen went well."
Weiss also said that left fielder Carlos Gonzalez, who has a sprained UCL in his right middle finger, has been taking some swings.
"He hasn't hit off a pitcher, but he's feeling better," Weiss said.
Steve Dorsey is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.