Try using silicone muffin cups. The muffins pop right out, and you save the planet and money by not having to purchase paper liners. They wash easily, too. I got mine for a little over $3 at A.C. Moore with a coupon.
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I have found that using silicone mats for baking is the best. However, these sheets aren't the easiest things to store when you are done with them. So my solution to this dilemma was to use an empty paper towel roll and roll the silicone sheet up and stuff it inside.
Silicone pans can be difficult to handle when full of batter or dough. So when using silicone bake ware I put the silicone pan on an upside down cooling rack before filling it with batter or dough.
My solution is to simply put the damp mats right back into the oven on oven racks. Most likely, the oven will be warm from baking anyway, and the mats dry nice and flat in no time.
