These enemies appear in some locations. This page in our guide to Sekiro: Shadows Die Twice will show you a simple way in which you can deal with these foes.
Loaded Axe is a perfect tool for killing enemies equipped with shields. You can get this prosthetic tool early in the game - examine the starting areas of Hirata Estate. Find Shinobi Axe of the Monkey and then go to the Sculptor. Remember to put the Loaded Axe into one of the three slots for your prosthetic.
All steps for crafting this item are described in the Prosthetic Tools chapter.
Lock your camera on an enemy carrying a shield. This will reduce the risk of missing your attack - Loaded Axe is a rather slow weapon. A shield will shatter with one hit, revealing the enemy.
Loaded Axe uses 2 Spirit Emblems. Luckily, shielded enemies are usually found in pairs. If you can't use Loaded Axe, switch to, e.g. Shinobi Firecrackers. You can also wait for that enemy to make a move - dodge it to attack the enemy from a side or from the back.