In some aspects, the present disclosure pertains to self-expanding emboli-capturing centering devices for centering a medical instrument in a conduit within a patient. The centering devices comprise (a) an elongate shaft, (b) a self-expanding centering member having an open distal end and an inner surface forming a central lumen with a flared distal portion, the centering member being configured such that a fluid flowing in a distal-to-proximal direction that is received by the open distal end flows proximally along the flared distal portion of the central lumen before exiting the central lumen through one or more openings in a proximal portion of the centering member, and (c) a filter material configured to filter the fluid received by the open distal end of the centering member. Other aspects of the present disclosure pertain to systems and methods employing such centering devices.