What happens if you call erase() on a map element while iterating from begin to end?

Question

C++11

This has been fixed in C++11 (or erase has been improved/made consistent across all container types).
The erase method now returns the next iterator.

auto pm_it = port_map.begin();
while(pm_it != port_map.end())
{
    if (pm_it->second == delete_this_id)
    {
        pm_it = port_map.erase(pm_it);
    }
    else
    {
        ++pm_it;
    }
}

C++03

Erasing elements in a map does not invalidate any iterators.
(apart from iterators on the element that was deleted)

Actually inserting or deleting does not invalidate any of the iterators:

Also see this answer:
Mark Ransom Technique

But you do need to update your code:
In your code you increment pm_it after calling erase. At this point it is too late and is already invalidated.

map<string, SerialdMsg::SerialFunction_t>::iterator pm_it = port_map.begin();
while(pm_it != port_map.end())
{
    if (pm_it->second == delete_this_id)
    {
        port_map.erase(pm_it++);  // Use iterator.
                                  // Note the post increment.
                                  // Increments the iterator but returns the
                                  // original value for use by erase 
    }
    else
    {
        ++pm_it;           // Can use pre-increment in this case
                           // To make sure you have the efficient version
    }
}

Here's how I do that ...

typedef map<string, string>   StringsMap;
typedef StringsMap::iterator  StrinsMapIterator;

StringsMap m_TheMap; // Your map, fill it up with data    

bool IsTheOneToDelete(string str)
{
     return true; // Add your deletion criteria logic here
}

void SelectiveDelete()
{
     StringsMapIter itBegin = m_TheMap.begin();
     StringsMapIter itEnd   = m_TheMap.end();
     StringsMapIter itTemp;

     while (itBegin != itEnd)
     {
          if (IsTheOneToDelete(itBegin->second)) // Criteria checking here
          {
               itTemp = itBegin;          // Keep a reference to the iter
               ++itBegin;                 // Advance in the map
               m_TheMap.erase(itTemp);    // Erase it !!!
          }
          else
               ++itBegin;                 // Just move on ...
     }
}

This is how I would do it, approximately:

bool is_remove( pair<string, SerialdMsg::SerialFunction_t> val )
{
    return val.second == delete_this_id;
}

map<string, SerialdMsg::SerialFunction_t>::iterator new_end = 
    remove_if (port_map.begin( ), port_map.end( ), is_remove );

port_map.erase (new_end, port_map.end( ) );

There is something odd about

val.second == delete_this_id

but I just copied it from your example code.