When matching red clothes with other colors it is easier to work with darker red shades, such as brick red. Since red has violet and orange as analogous colors, shades of these colors often work well, especially when the colors are kept away from opposing levels of light or dark.
The compliment to red is green, and can make for a reasonable color match so long as you keep the colors muted. Otherwise you create an ugly clash as the colors make one another stand out far too much, or in unpleasant ways.
Be especially cautious in attempting to match red with blues and yellows.
See also: Color matching