It depends on the mat. When I had my OES, and when she was in full coat, I would spray mats with a watered down hair detangler product (I used Tame but don't believe it's made any longer) and rub it into the mat. Then I'd first try to remove it with a slicker. If the slicker failed I tried a pin bursh, and if that failed I then used a good rat tail metal comb. If all these failed I carefully cut the mat out with a small pair of blunt tipped scissors.
My secret? Corn starch. Work it in to the matted area as though it were baby powder. (It is much safer than the talc they use in powder.) Then start at the outer edge of the matt and work to detangle it - gently. It may require splitting the matt very carefully with a pair of scissors.
I use corn starch before I groom if they have much undercoat at all. It loosens the dead hair, the powder working like a lubricant. Grooming doesn't pull nearly as much.