Testing whether a matrix contains a submatrix
A few suggestions regarding the style:


There's no need for parentheses in the pattern matching blocks. Those are evaluated as tuples by the very fact that they are comma separated:

match smallValue = largeValue, widthIndex &lt; searchWidth with
| true, true  -&gt; WidthLoopRec heightIndex (widthIndex + 1)
| true, false -&gt; true 
| false, _    -&gt; false


and:

 match isMatch , heightIndex &lt; searchHeight with
 | true, true  -&gt; HeightLoopRec (heightIndex + 1)
 | true, false -&gt; true
 | false, _    -&gt; false

In HeightLoopRec, there's no need for isMatch. You can use the result of calling WidthLoop directly inside the pattern matching (maybe with parentheses to make it more legible):

match (WidthLoop heightIndex), heightIndex &lt; searchHeight with

The function HeightLoop is not needed and can be removed and replaced by its contents, making HeightLoopRec the top level function. This is obvious by its signature (unit -&gt; bool). It doesn't take anything as input, unlike its internal tail-recursive function whose signature is int -&gt; bool.
WidthLoop can be inlined (let inline WidthLoop heightIndex =).
I think it would be better to handle the exceptions before getting into the actual computation. In fact, if the code base is done in F#, there should be no null values (as those would be replaced by option types). Within your code domain, illegal values should be made unrepresentable, as the famous motto goes. 

This should also account for out-of-range indexing. If a mathematical operation makes no sense, the typing itself should not allow it to be made.

You could use FsCheck to test your code with random values to see that your code never raises exceptions. Logically, "no answer" should not be represented as false. If a function may return no value at all or a bool, then its return type should be bool option, where None would represent the lack of a valid result.
Your function name should probably reflect more clearly their intention. I'm not a mathematician, but I guess you would mean something like isRowContained (instead of WidthLoop), or whatever makes sense.