The chances of the final seasons of both shows airing in your area are quite good. However, they'll be airing in reruns.
I'm afraid you've missed the boat on this one: The final seasons of TNT detective show "Rizzoli & Isles" and USA medical show "Royal Pains" came and went nearly a year ago.
However, "Rizzoli & Isles" aired 105 episodes across seven seasons, and "Royal Pains" aired 104 episodes across eight seasons, meaning they're both likely to end up in syndication for a long time to come (the general rule of thumb is that a show needs to have at least 100 episodes to be a good candidate for rerunning). Indeed, "Rizzoli & Isles" episodes are already being rerun on broadcast affiliates around the country, and "Royal Pains" reruns are appearing on the Universal HD and CLOO cable channels.
The "Royal Pains" series finale aired in July, and the "Rizzoli & Isles" finale in September. Since both were on cable, they aired everywhere in North America, so either you missed them or you didn't realize that what you were seeing was really the end.
The latter case would be unfortunate, since the writers tried hard to give a neat and satisfying ending to both shows (a rare luxury in the TV biz).
"The biggest debate in the room was whether Hank should end up in the Hamptons, or elsewhere," "Royal Pains" head writers Andrew Lenchewski and Michael Rauch said in a joint interview with Deadline.com. "It was a pretty polarizing debate, with everyone bringing very strong arguments to the table." I won't say what they decided so as to not spoil things for you.
As for "Rizzoli & Isles," TNT boss Kevin Reilly said ending the show after seven seasons was a mutual decision among everyone involved. "It felt like it was time. Everybody felt good about that."
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