Option 1 is Wednesday, July 31, against the White Sox at 7:05 p.m. ET.
Option 2 is Friday, Sept. 6, against the Mets at 7:05 p.m.
"We are always striving to provide our fans the best experience possible at Progressive Field and wanted to make it right for the fans who endured the lengthy weather delays and ultimate after-midnight restart," Shapiro said Monday in a statement. "By providing make-up opportunities on either July 31st or September 6th, which will both include Sugardale Dollar Dogs and postgame fireworks, fans will have the opportunity to have a positive and memorable ballpark experience."
Ticket exchanges for either game must be redeemed by July 1.
"We value each and every one of our fans and want to thank them for staying at some or all of the May 31st game," Shapiro said. "We appreciate their loyalty, patience and perseverance."
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.