Does Up have a post-credit scene?

Up has no post-credits scene. Once the final card passes, that is the film. There is no stinger, no sequel tease and no extra gag waiting at the bottom of the roll.

What there is, and what genuinely rewards sitting through, is the credit sequence itself. Up is built around Ellie's My Adventure Book — the scrapbook Carl carries for the whole film believing the second half is blank, until he opens it in the third act and finds she had filled it with photographs of their marriage, under the heading 'Stuff I'm Going to Do', with a note telling him to go and have a new adventure. The credits are that instruction being carried out. They are designed as pages from Carl's own scrapbook: Carl and Russell at the badge ceremony, at baseball games, eating ice cream, with the dogs, with the house. It is the film showing you that Carl did not simply survive his grief — he started a second life and documented it the way Ellie taught him to.

So the credits function as an epilogue in the same way WALL·E's do, without technically being a post-credits scene. If you are watching with someone who cries at the opening montage, the credits are the part that repairs the damage, and walking out early means the film ends on a cliff-top instead.

One footnote for completists: Dug's Special Mission, a short film about what the dogs were doing before Carl and Russell arrived, was made for the home release rather than attached to the theatrical print, so it never played after the credits in cinemas.