Disclosed herein are systems and methods for protecting a subject from embolisms during TAVI and other percutaneous valve procedures. Some embodiments include two flexible catheters designed to pass over a guidewire into two separate arteries, such as carotid or innominate arteries, each flexible catheter including a vessel blocking mechanism and a bypass feature that prevents ischemia while the vessel blocking mechanism is in use. Other embodiments include a single, bifurcated flexible catheter having two arms, each of which is configured to protect a different artery. In some embodiments, each arm includes a vessel blocking mechanism and a bypass feature that prevents ischemia while the vessel blocking mechanism is in use. In some embodiments, the systems also may include one or more concentric guidewires.