This doesn't fully answer the question but I think it will give you what you need to get it. Give it a try. Place the following code in a new moudule:
Public Sub FindStrings()
Dim rng1 As Excel.Range
Dim rng2 As Excel.Range
Set rng1 = ActiveSheet.Range("A1")
Set rng2 = ActiveSheet.Range("A2")
Dim i As Integer
Dim j As Integer
Dim searchVal As String
For i = 3 To Len(rng2)
For j = 1 To Len(rng1)
searchVal = Mid(rng1, j, i)
If Len(searchVal) < i Then Exit For
If InStr(1, rng2, searchVal) Then Debug.Print searchVal
Next j
Next i
End Sub
In cell A1 put example.net/test
In cell A2 put www.test.com
Result
tes
est
test
UPDATE
I updated the code to search for a minimum of 4 characters instead of 3 (as you mentioned above). Furthermore, I guessed you wouldn't want strings such as www. and .com returned, nor strings with the / or . character. So the code pulls those out as well. Also, it compares every column combination.
Option Explicit
Public Sub CompareStrings()
Dim Arr As Variant
Dim i As Integer
Dim j As Integer
Dim StartRange As Excel.Range
Dim SearchRange As Excel.Range
Dim Counter As Integer
Dim ComparableRange As Variant
Dim Comparable As Integer
Dim Compared As Integer
Dim SearchVal As String
Set StartRange = ActiveSheet.Range("A1")
Counter = 0
For Each ComparableRange In ActiveSheet.Range("A1:A2")
Set SearchRange = Range(StartRange.Offset(Counter), Cells(StartRange.Offset(Counter).Row, Columns.Count).End(xlToLeft))
Arr = Application.Transpose(Application.Transpose(SearchRange.Value))
Debug.Print "Row " & SearchRange.Row & ":"
For j = LBound(Arr) To UBound(Arr)
For i = j + 1 To UBound(Arr)
For Comparable = 4 To Len(Arr(j))
For Compared = 1 To Len(Arr(i))
SearchVal = Mid(Arr(j), Compared, Comparable)
If InStr(1, SearchVal, ".") = 0 Then
If InStr(1, SearchVal, "/") = 0 Then
If Len(SearchVal) < Comparable Then Exit For
If InStr(1, Arr(i), SearchVal) > 0 Then Debug.Print vbTab & SearchVal
End If
End If
Next Compared
Next Comparable
Next i
Next j
Counter = Counter + 1
Next ComparableRange
End Sub
When comparing test.com/q=age with another.com?q=age You will still get results such as:
q=ag
=age
q=age
...though I suspect you only want the third one. The longer the matching strings are the more results you will get. The last results are the ones you will probably want.