I was recently reminded of an anime I saw between 2000 and 2002 on VHS. The actual production date was probably from late 1980s, a la Bubblegum Crisis (but not actually, I checked), to the mid 1990s. I thought it was Neon Genesis Evangelion, but based on images I could find, the characters I remember in the scene do not exist in that show, nor was it the previously mentioned Bubblegum Crisis.
The scene I remember has a short, black-colored robot warning a long-haired blonde girl, and they duck into a stairwell. She asks: "Here, black exil?"; ("Exil", being a shortened word for what the robot is actually called, it is really a suit that can transform and be worn by the previously mentioned character.) The robot then transforms into a suit that she wears, and they go off to fight whatever the warning was about.
Edit:
I've also ruled out Battle Skipper, the name was close with "Exstar", but the "robots" were autonomous tanks and not sentient suits.
Some further detail I remember is the girl may be dressed in a Japanese school uniform a la Sailor Moon, potentially an orange skirt or dress. (But that may be me confabulating it with Sailor Venus ¬.¬ )