Seems like male Robin does a pretty decent job of countering them, and Takumi as well, given that few of the many red sword characters have good resist. Similarly female Corrin and Nowi are good at beating them up, but being dragons means they get hit much harder than they really should because a lot of popular red characters incidentally do bonus damage to dragons. Azura is likely the best character in the game straight-up, so she would be amazing if you have her. As for budget options, Peri seems fairly solid since she handles physical and magic characters both in different ways, and Effie seems popular if a little tricky to use effectively since she's so slow.
Personally I get away without having a direct counter to sword characters by baiting them into first-hitting me with Takumi and Lyn. A Lyn at low health mops up most red characters, and virtually all of them if they have a little chip damage first (like from Camilla).