Try replacing core functionality with COM enabled .NET libraries. "Hollow out" your existing VB6 apps by moving functionality to .NET bit by bit.
Beware of complete rewrites. Though they are tempting "because it is a clean cut" - usually madness lays ahead! Read "Working Effectively with Legacy Code" by Michael Feathers as a preparation. Though the book does not specifically go into "moving from one language to another" it does show a lot of real world pitfalls you will encounter.
I do think that all developer should have defined time slots where they do migration work on the legacy apps they developed before. Since they already have domain knowledge and know the problem space they should be the most productive.
