Anchovies and dishes with Anchovies in them are extremely salty. Therefore you want to pair them up with chilled white wines that are high in acidity, and lightly oaked.
A Sauvignon Blanc from New Zealand would work beautifully, as it is pungent on the nose like anchovies are, but the flavours are tangy and crisp making it quite refreshing.
Sweet wines with a high acidity are another option as they help balance the salt of the Anchovies and a higher acidity helps the wine stand up to the intensiveness of the anchovies. A German Riesling would be exceptional in this case, as would and off-dry or semi-sweet Riesling.
Beer and Pilsner
If you’re interested in a Beer Pairing for Anchovies, Pilsner is excellent as it has a sweet bread like quality as well as refreshing finish that works with the saltiness of the Anchovies.