The Intimina Lily Compact is the only menstrual cup (that I've seen) that folds up to carry easily with you in your purse or clutch. Because of its small size, it should only be used with light to medium flow (or emptied more regularly), but because it folds so compactly it's a perfect "emergency cup" to carry with you regularly in case your time sneaks up on you. Like normal sized cups, it's made of medical grade silicone and is completely safe and comfortable to wear. It has ribbing throughout the cup which allows it to collapse, but when it's extended it is what keeps the cup in place during your period. It has a short, ribbed stem that should simplify removal.
Unfortunately, it's on the expensive end of the spectrum for menstrual cups. But that expense might be worth it if you'd rather carry around a small, discrete box than a large, obvious pad as a backup.