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.
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 ¬.¬ )