While we're talking about women in sport, Elizabeth I inherited an enthusiasm for tennis, both as a spectator and player, from her father. In the 16th century, though, it was an indoor game--today called "real tennis" to distinguish the original form from its modern outdoor successor, "lawn tennis."
Henry V was also a tennis enthusiast. The scene in the Shakespeare play where the Dauphin of France sends him a box of tennis balls as an insult to remind him of his frivolous youth wasn't an anachronism, though it probably didn't actually happen that way. (Though when Harry responds, "When we have match'd our rackets to these balls, / We will, in France, by God's grace, play a set," that was an anachronism--they didn't use rackets in his day.)