They did - in fact, it was a standard feature of Medieval warfare that captured combatants of means could arrange for a ransom to buy their freedom from captivity. Though as you'll see, the practicalities depend on whether it's a common soldier or an aristocrat who's doing the capturing. More can always be said on the matter, of course, but since warfare of all stripes is ever popular on the sub, the following previous posts may interest you:

• u/MI13 has an excellent overview on the matter, and don't overlook the discussion in the comments - that thread's a goldmine;
• u/Lhyon outlines the general process of ransom;
• and u/The_Truthkeeper examines one specific case of a French knight captured at Agincourt, and how the arrangements were made for him.

A few more relevant threads in next post because argh tag limit.