Lord Arundel married Lady Elizabeth Stuart, daughter of Esme Stuart, 3rd Duke of Lennox, on 7 March 1626. They had nine sons and three daughters:
Thomas Howard, 5th Duke of Norfolk (1626/27–1677), died without issue
Henry Howard, 6th Duke of Norfolk (1628–1683/84), had issue; (ancestor of 7th through 9th Dukes of Norfolk)
Hon. Philip Howard (1629–1694), Catholic Cardinal
Hon. Charles Howard (1630–1713), married Mary Tattershall (d. 1695), had issue, including Henry Howard of Greystoke; who married Mary Aylward (d. 1747), had issue, including Charles Howard, 10th Duke of Norfolk (through whom Charles Howard, 11th Duke of Norfolk was also descended);
Lady Anne Howard (1632-?)
Lady Catherine Howard (1634-1655)
Hon. Talbot Howard (1636-?)
Hon. Edward Howard (1637-1691), married Anne Wilbraham, had issue. Edward's great-grandson Thomas Howard (1736-1824), a Quaker, renounced succession c.1812; succession then passed to the issue of Hon. Bernard Howard of Glossop (below).
Hon. Francis Howard (1640-1722)
Hon. Bernard Howard of Glossop (1641–1717), married Catherine Tattershall (d. 1727, sister of his brother Charles' wife, Mary) and had issue, including Bernard Howard II of Glossop, who married Anne Roper (d. 1744), had issue, including Henry Howard of Glossop and Sheffield, who married Juliana Molyneux, had issue, including Bernard Howard, 12th Duke of Norfolk (from who all subsequent Dukes of Norfolk descend) and Lord Henry Howard-Molyneux-Howard;
Hon. Esme Howard (1645–1728), had one daughter, who died unmarried
Lady Elizabeth Howard (1651-1705)
Hon. John Howard (1652-1711)