I have created a relationship, so that a portal shows records where Company are the same, and Date Despatched are the same.

When I view the portal the relationship works, when showing the records where company and date despatched are the same.

However, when the Company are the same and the Date despatched are both empty it does not show these records, it only works when date despatched has a valid matching date.

Is there a way to make it show records when both Date Despatched are the same but empty?

You need a calculation field (in the child table) to fulfil your logic, then use the new field as the target of the relationship. Effectively your calc field is a combination of the two other fields.

A global field in the parent table should suffice for the other side.

Relationships do not consider empty fields as matching. You could define a calculation field like:

Case ( IsEmpty ( DateDespatched ) ; 1 ; DateDespatched )

and use it instead.