the best antenna close to a patch is the annular ring (also called loop) antenna. patch antenna resonates at λ/2 distance. for loop antenna this is approximately λ/4.
if you make the width of the transmission line in loop antenna narrow, you can make its size smaller and smaller (since the currents flow approximately from the middle of transmission line).
if you make the width larger, it is better for bandwidth. in the limit, as the width increases, the loop antenna would behave like a patch.
you can think of meandering as making the loop longer and longer. the problem is, as you meander more and more, in a compact space, the transmission lines couple to each other. also bandwidth is usually small. and of course, currents usually cancel each other resulting in lower gains.