For the tempura: Heat a deep fryer filled with vegetable oil to 375 degrees F. Line a sheet pan with paper towels.
Combine the flour, water, yellow mustard, if using, and baking powder in a bowl. Whisk the ingredients together until smooth. Pat the herring fillets dry with some paper towels, then dredge in the batter.
Gently lay the battered herring into the fryer. Cook until it turns a nice golden brown, then lift out of the fryer and lay on the prepared sheet pan to cool. Salt generously with while the fish is still hot.