Robert Catesby was married in 1593 (when he was about 21) to Catherine Leigh who was, rather ironically, a daughter from the wealthly Protestant family of Sir Thomas Leigh of Stoneleigh Abbey in Warwickshire (they were fairly close neighbours of the Catesbys). Catherine brought him a good dowry and also a good Protestant connections which protected him somewhat from Elizabeth I's recusancy laws. They had at least two children, William and Robert but I'm not sure what became of them. However Catherine, his wife, died in about 1598 - her death may well have hardened his religious views - so at the time of the Gunpowder Plot he was a widower but possibly with two sons under 10 years of age (although doubtless their care was entrusted to an aunt, sister or cousin).
EDIT - Regarding the two boys, it seems that the first, William, died soon after birth but Robert, who was baptised at Chastleton's Protestant church on 11 November 1595, seems to have survived childhood and possibly married a daughter of Thomas Percy, that's the Thomas Percy who died alongside Robert Catesby in the shoot-out at Holbeche House.
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