Contract Based Programming vs Unit Test

I am a somewhat defensive programmer and a big fan of Microsofts Code Contracts.

Now I cannot always use C# and in most languages the only tool I have is assertions. So I usually end up with code like this:

class
{       
    function()
    {   
         checkInvariants();
         assert(/* requirement */);

         try
         {
             /* implementation */
         }
         catch(...)
         {
              assert(/* exceptional ensures */);                  
         }
         finally
         {
              assert(/* ensures */);
              checkInvariants();
         }
    }

    void checkInvariants()
    {
         assert(/* invariant */);
    }
}

However, this paradigm (or whatever you would call it) leads to a lot of code cluttering.

I have started to wonder if it is really worth the effort and whether proper unit test would already cover this?