As swain, Try and go for extended auto-attack fights with him as you will win those. But try repositioning so he cannot easily land his Q or E on you.

Post 6, when he activates his Ultimate, unless you can kill him quickly, just disengage and wait for it to time out.

Keep the minion wave closer to your side of the map. Swain is easy to kill early if he is over extended.

Invest in some form of healing reduction to make killing him easier early on.
 As swain, Try to go for prolonged automatic attack fights with him that you will win those. But try to reposition so that he can't easily place his Q or E on you. Post 6, when he activates his Ultimate, unless you can kill him quickly, just disengage and wait for that time no longer. Keep the minion wave closer to your side of the map. Swain is easy to kill early if it's too wide.