The Carrick mat, while easy to tie, tends to be a bit small for our purposes: you want to tie your trivet out of thin rope so pots full of hot deliciousness don't spill on your table and you want it to be wide to support the whole base of the pot, but the Carrick mat is too small relative to the thickness of the rope you use to be remarkably useful. I made a four-pass carrick mat (most of my mats are three pass) and it was a good size but didn't have quite enough structure to maintain its shape well. See it in the third picture, below. Nonetheless, it is a very good and simple introduction into tying rope mats and can be used for things other than trivets. You also might try tying one using paracord and seeing if the result is suitable for a coaster.
More traditional rope mats include the Ocean Plait mat
and the Oval mat. The Ocean Plait mat is the most recognizable of the rope mats and you can see it in the first picture below. That one is made of slightly thicker rope (3/8" instead of 1/4") than I used for most of these and I took four passes instead of three. Four passes gives an excellent fullness to the finished mat, but with the thicker rope it was a bit too big for a trivet...I use it as a doormat.
The oval mat (second picture) makes an excellent trivet but it can be a bit difficult to work into an even shape. It works extremely well because it's quite large compared to the diameter of the rope used and it's distributed evenly...there are no big holes anywhere. It's also one of two knots that I consistently have to attempt more than two times to get right, so make sure you find a good guide for it and bring along a second helping of patience.
You can find detailed instructions for how to tie these mats in the books I list at the end of this instructable or in many places online.