There is no way to know for sure in an absolute sense. By the way, the term AROMATIC implies that the molecule is planar because it's part of the definition.
The only way to know for sure that it's planar or non-planar is to know that the steric and angle strain overcomes the stability attained by aromaticity (hence planar). In other words, the stability attained by adopting a non-planar conformation is greater than the stability attained by adopting a planar conformation (thus being aromatic).
At the end of the day, it's a quantitative matter.....
Of course, knowing that there is some steric strain makes it a tad suspicious. Thus, if you were given bicyclic conjugated molecules with a huckel number.....you'd probably go with something along those lines if asked which of the following is aromatic.