Pattern to avoid nested try catch blocks?

Just to offer an "outside the box" alternative, how about a recursive function...

//Calling Code
double result = DoCalc();

double DoCalc(int c = 1)
{
   try{
      switch(c){
         case 1: return Calc1();
         case 2: return Calc2();
         case 3: return Calc3();
         default: return CalcDefault();  //default should not be one of the Calcs - infinite loop
      }
   }
   catch{
      return DoCalc(++c);
   }
}

NOTE: I am by no means saying that this is the best way to get the job done, just a different way

You could flatten out the nesting by putting it into a method like this:

private double calcStuff()
{
  try { return calc1(); }
  catch (Calc1Exception e1)
  {
    // Continue on to the code below
  }

  try { return calc2(); }
  catch (Calc2Exception e1)
  {
    // Continue on to the code below
  }

  try { return calc3(); }
  catch (Calc3Exception e1)
  {
    // Continue on to the code below
  }

  throw new NoCalcsWorkedException();
}

But I suspect the real design problem is the existence of three different methods that do essentially the same thing (from the caller's perspective) but throw different, unrelated exceptions.

This is assuming the three exceptions are unrelated. If they all have a common base class, it'd be better to use a loop with a single catch block, as Ani suggested.

As far as possible, don't use exceptions for control flow or unexceptional circumstances.

But to answer your question directly (assuming all the exception-types are the same):

Func<double>[] calcs = { calc1, calc2, calc3 };

foreach(var calc in calcs)
{
   try { return calc(); }
   catch (CalcException){  }
} 

throw new NoCalcsWorkedException();