Embolic material capture catheters and related devices and methods employ a staged deployment of an embolic material capture element. A method of deploying an embolic material capture element in a blood vessel includes advancing the embolic material capture element in an insertion configuration through the blood vessel. A middle portion of the embolic material capture element is expanded via distal advancement of an inner sheath toward a distal end portion of the embolic material capture element constrained by a dilator assembly. The dilator assembly is then reconfigured to release the distal end portion of the embolic material capture element from engagement with the dilator assembly. Upon release, the distal end portion of the embolic material capture element expands to complete deployment of the embolic material capture element in the blood vessel.