Given that so far in the series we have only had subtle hints at how powerful Mihawk is is it reasonable to assume that he has power equivalent to that of a yonko say Kaido since parallels between him and shanks are done quite often?
In Marineford, he fought Vista (one of the top officials of the Whitebeard Pirates) to a draw, also Jozu, another of Whitebeard's top brass, was able to deflect his attack unharmed. I don't think he is on par with the Yonkou, although he was Shanks' rival when they were younger, he lost interest on dueling him after Shanks' lost his arm, but that doesn't mean he's as strong or stronger. He respects him enough to pull back from the war once he showed up on Marineford saying fighting Shanks wasn't part of the agreement. So I'd say he's pretty much a little bit under Yonko level, probably on par with Admirals.