Well you are correct that using the opposite color of another color does 'compliment' one another. That is why they are called "complimentary" colors.Yellow & Purple, Blue & Orange, Green & Red.
Using bronze, warm browns, copper, & other colors that have similar undertones are sure to make those blue eyes pop!
But using colors that are close to each other on the color wheel can also be pleasing to ones eye. Such as, blue & red make purple, so a deep purple eye liner will help make your blue eyes seem even brighter! Blue & yellow make green, so may be you should look into green eye shadows with a dark brown eye liner (or vise versa, green eye liner with a copper eye shadow).
However, you should also consider the 'shape' of your eyes as well. I would highly suggest visiting www.MaryKay.com, & try out their virtual makeover! It's fast, easy & free! I would suggest choosing a model instead of uploading your own picture, so you don't have to sign up for anything, & you can play as long as you like. Just choose which model shares the same eye shade as you (or as close as you can get) then start playing with eye shadows & eye liners! You can virtually see which colors make them pop & which ones don't, without having to keep putting on & taking off makeup.
Sorry for the many paragraphs! Good luck, & best wishes!