These were all received in 1998 unless otherwise noted.

- Blockbuster Entertainment Awards -

Won a Blockbuster Entertainment Award for Favorite Supporting Actress in a Sci-Fi (Winona Ryder). Nominated for another one under Favorite Actress in a Sci-Fi (Sigourney Weaver).

- Golden Satellite Awards -

Nominated for a Golden Satellite Award in Best Motion Picture in Animated or Mixed Media.

- Academy of Science Fiction, Fantasy, and Horror Films -

Nominated for six Saturn Awards under Best Actress, Best Director, Best Costumes, Best Special Effects, Best Science Fiction Film, and Best Supporting Actress.