Growing up in the province, I remember it was such a struggle to find a good product that could effectively remove make-up. One of the reasons that also contributed to the dilemma was that back then, there wasn't a lot to choose from, in the first place. But now, it's a completely different story. There's just many products to choose from, from different brands from different countries.
My ultimate favorite make-up remover would be Bifesta's Micellar Water. However, when I do need something stronger to wipe out waterproof makeup such as heavy duty liquid lippies, this recent discovery of mine does the job pretty well. Pond's washable cold cream is a product from Japan, but luckily, it's currently available in Watsons :) One of the things that I really love about this is the fact that it contains Witch Hazel, which simply has many uses for the skin.
What I do is that I apply a scoop out a generous amount using a cotton bud/spatula, then place it all over my face. Afterwards, I remove the make-up using cotton, then I wash it off since it's washable anyways. Right after that, I proceed with my usual cleansing routine. Let me be the one to tell you that it's good enough for my liquid lipsticks, which are such a pain to remove! So this product is really worth the price and the jar is really big, so it might take a while before you consume an entire one.