Another hint (although probably not applicable to this situation, as there are no other trains on the Netherlands-Düsseldorf relation): If your train is already delayed at your departure station and there is another train which will most likely enable you to catch your connecting train somewhere else, just check with the information counter of your departure station. They will most likely stamp your ticket with "Zugbindung aufgehoben" (train obligation revoked) so as to enable you to take the other train to make your connection (at least they usually do in germany). Should you miss your connection which in turn leads to a total delay of more than one hour, they have to pay compensation, so it is entirely in their interest to enable you to make the connection.
If you have already missed your train (or decide to take a train of a higher category to minimize your delay), I wouldn't use the information counter (or Service Point, as they say) but instead simply jump onto the next train. If you explain the situation to the conductor, everything will usually be fine. If they don't believe you, ask them to check with the dispatchers ("Transportleitung") and if they still want to charge you for the fare difference, demand that they note your name on the ticket, confirm everything with a clipper print (ask for a "Zangenabdruck") and later hand everything in to the "Servicecenter Fahrgastrechte" which is responsible for compensation and refund matters in such cases.