I would just bypass the contour altogether. It seems that you essentially want to find the points where
(Am1_r == 0) & (Am2_r == 0)
A little fancy logical indexing would allow you to do this without any contour plot needed. First, two things to note
1. You should probably interpolate your data a bit - 51-by-51 seems rather coarse. interp2 will help you to do this
2. Comparing to zero (as I've shown above) is not always the best idea. Typically you want to make your condition such that the magnitude is less than some threshold.
Here's a quick example for ya...
x = linspace(-1,1,51);
y = linspace(-1,1,51);
[X,Y] = meshgrid(x,y);
Z1 = X.^2 + Y.^2 - 0.5;
Z2 = (X + Y)/2;
xnew = linspace(-1,1,1000);
ynew = linspace(-1,1,1000);
[XNew,YNew] = meshgrid(xnew,ynew);
Z1 = interp2(X,Y,Z1,XNew,YNew);
Z2 = interp2(X,Y,Z2,XNew,YNew);
threshold = 1e-3;
z1NearZero = abs(Z1) < threshold;
z2NearZero = abs(Z2) < threshold;
allConditionsMet = z1NearZero & z2NearZero;
xpoints = XNew(allConditionsMet);
ypoints = YNew(allConditionsMet);
result = [xpoints,ypoints]
[r,c] = find(allConditionsMet)
Note that I have defined an x and y scale, which you would probably find helpful to do as well.
Hope this helps!