Approximate proof labeling schemes were introduced by Censor-Hillel, Paz and Perry. Roughly speaking,
a graph property P can be verified by an approximate proof labeling scheme in constant-time if the vertices of a graph having the property can be convinced, in a short period of
time not depending on the size of the graph, that they are having the property P or at least
they are not far from being having the property P. The main result of this paper is that bounded-degree planar graphs (and also outer-planar graphs, bounded genus graphs, knotlessly embeddable graphs etc.) can be verified by an approximate proof labeling scheme in constant-time.