Radiopaque cobalt-based alloys having a smooth electropolished surface with rounded edges and methods for electropolishing such alloys. A cobalt-based alloy includes cobalt, chromium, and one or more radiopaque elements. In one embodiment, examples of radiopaque elements include so-called platinum group metals (i.e., platinum, palladium, ruthenium, rhodium, osmium, or iridium). Group 10 elements (i.e., platinum or palladium) are particularly preferred. Because of the presence of the platinum group metal(s), such alloys are generally difficult to electropolish. Electrolyte formulations and methods for electropolishing such alloys are also disclosed.