PHP - How to catch a 'Trying to get property of non-object' error

try..catch works on thrown exceptions. Errors are not exceptions. You can silence errors, but please don't do that. Instead, properly check what you're getting:

$result = Model()->find('id=1');
if ($result) {
    $id = $result->id;
} else {
    // handle this situation
}

The model needs to be able to throw an exception.

Here's what your model might look like:

class Model{

   public function find($id){
      $result = //do stuff to find by id

      if (!isset($result)){
          throw new Exception("No result was found for id:$id");
      }
      return $result

   }
}

Then you would use your try/catch block:

try{  

    $id = Model()->find('id=1')->id;

}catch(Exception $e){
    echo 'failed';
}

However, exceptions should only be thrown under "exceptional" circumstances. I don't think using exceptions to direct program flow is the right way to go about it.

Having said that, if returning a NULL when you attempt to retrieve the ID property is an exceptional situation, then exceptions are certainly suitable.