I have a dataset and would not want Mathematica to interpolate at all while plotting the contours. This is because the data contains essential binning information and the "steps" in the contour must convey that sense. Interpolating on the data to "smoothen" the contours would make the plot lose its physical validity altogether. Apparently, ListContourPlot doesn't show the contour lines at all when InterpolationOrder is set to 0.

ListContourPlot[data, ScalingFunctions -> {"Log", "Log", "Log"}, InterpolationOrder -> 0, Contours -> {Log[3]}, ContourShading -> {None, GrayLevel[0.5, 0.36]}, GridLines -> {{0.001, 0.01, 0.1, 1}, {5*10^-4, 10^-3, 2*10^-3, 5*10^-3}}, ContourStyle -> {Thick, Black}] 

With just the InterpolationOrder commented out the contour lines do appear.

 ListContourPlot[data, ScalingFunctions -> {"Log", "Log", "Log"}, (*InterpolationOrder -> 0,*) Contours -> {Log[3]}, ContourShading -> {None, GrayLevel[0.5, 0.36]}, GridLines -> {{0.001, 0.01, 0.1, 1}, {5*10^-4, 10^-3, 2*10^-3, 5*10^-3}}, ContourStyle -> {Thick, Black}] 

What I want is that neither of the regions be shaded but the contour line appear. Which I believed I should get with the code,

ListContourPlot[data, ScalingFunctions -> {"Log", "Log", "Log"}, InterpolationOrder -> 0, Contours -> {Log[3]}, ContourShading -> None, GridLines -> {{0.001, 0.01, 0.1, 1}, {5*10^-4, 10^-3, 2*10^-3, 5*10^-3}}, ContourStyle -> {Thick, Black}] 

But this gives me just nothing. A blank plot.

A sample dataset may be obtained using,

 data = List[{10^-4, 10^-3, Abs[-0.5*Log[10^-4/10^-3]]}]; Do[ Do[ test = Abs[-0.5*Log[i/j]]; data = Join[data, List[{i, j, test}]], {i, 10^-4, 10^-2, 10^-3}], {j, 10^-3, 6, 10^-1}];