Thus an heir presumptive does not hold an heir's title, if any.
(See below about heir's titles.) If a peer dies leaving a wife but no son, the heir inherits unless the widow says she might be with child. If she stays silent, it is assumed that she is not.
The eldest son is called the heir apparent, since he is clearly the heir.
If there is no such son, the next in line is called the heir presumptive since, no matter how unlikely (the duke is actually an ancient Benedictine Monk on his death bed) the possibility of a closer heir being created is still there.
His wife is the Countess of Saxonhurst, or Lady Saxonhurst, and she will sign herself Minerva (or Meg -- viz Forbidden Magic -- Saxonhurst.
An heir must be legitimate at birth to inherit a title, though that could mean a marriage ceremony performed while the mother is in labor.
Note, however, that courtesy titles (those held by heirs) do not give seats, or any of the other privileges of the peerage.
Most peers do not use their surnames as their title. " NOTE that the duke will also have a family name, ie.
There are a very few titles that can pass to a female if there is no direct heir, but they will revert to the male line when the lady bears a son.
(Such as the monarchy.) Some titles can automatically pass through a female heir (when there is no male heir) and most can be revived by subsequent generations by petitioning to the Crown. If your plot depends on something unusual, please do research it thoroughly before going ahead.