The current implementation of Delaunay interpolator returns NaN for grids whose x or y has dimension 1 (i.e. when you try to interpolate along a horizontal/vertical line, or in a single point). See example below.

By looking at the code, it seems that this can be fixed by simple rearrangement of calculations.
Suggested patch provided here: https://github.com/AmitAronovitch/matplotlib/commit/f312d864da9c72681eb3db3b5920ae64793c713e (let me know if you want a pull request).
The suggested implementation is almost identical. It might actually perform faster in some cases (there is one less multiplication op in the inner loop). There might be some differences in accuracy, but I believe they should only become observable in cases where the grid size is very large (which would probably cause memory problems anyway).

Example (before suggested patch):

>>> from matplotlib.delaunay import Triangulation
>>> tri = Triangulation([0,10,10,0],[0,0,10,10])
>>> lin = tri.linear_interpolator([1,10,5,2.0])
>>> # 2x2 grid works fine
>>> lin[3:6:2j,1:4:2j]
array([[ 1.6,  3.1],
       [ 1.9,  2.8]])
>>> # but not when 1x2, 2x1, 1x1:
>>> lin[3:6:2j,1:1:1j]
array([[ nan],
       [ nan]])
>>> lin[3:3:1j,1:1:1j]
array([[ nan]])
>>>

After suggested patch:

>>> from matplotlib.delaunay import Triangulation
>>> tri = Triangulation([0,10,10,0],[0,0,10,10])
>>> lin = tri.linear_interpolator([1,10,5,2.0])
>>> # 2x2 grid: same same
>>> lin[3:6:2j,1:4:2j]
array([[ 1.6,  3.1],
       [ 1.9,  2.8]])
>>> # but these work now
>>> lin[3:6:2j,1:1:1j]
array([[ 1.6],
       [ 1.9]])
>>> lin[3:3:1j,1:1:1j]
array([[ 1.6]])
>>>