I was a solid Arminian until a couple years ago. I'd say to challenge their view of the sovereignty of God. I was guilty of saying that God couldn't (fill in the blank) until I was challenged. The God of Abraham, Isaac and Jacob, the God who parted the Red Sea, the God who is enthroned in Heaven is able to do whatever He pleases.
Most Arminian teaching takes a very man-centered approach to salvation. But the Bible says that "In the beginning... GOD" We need to be open and offer answers to the questions that come up. Many come up in this very forum, as well as the general apologetics. I am not a firm believer in a setting that pits one Christian against the other, for when one person takes the offensive position, the other instinctively takes a defensive position.
Also, when an Arminian begins to accept the Biblical-ness of Calvinism, they can be very angry. I felt betrayed by everyone who ever held any sort of leadership role in the churches I grew up in for not telling me about this. I judged them and began to get very heady, believing I was better than them. Honestly, I should have been thrown into a cage until I got over it.
This is one of those dicipleship times. We need to be gentle and loving with these people, showing them the love within the doctrines of grace. We need to correct them, and remind them to remain humble through the process. We need to forgive them in advance, for I can't think of anyone I have ever discussed this matter with who didn't get abusive. All of this requires prayer, that the Holy Spirit would reveal the love of God to them and that He would give us a serving heart to withstand the emotion.
Anyway, that's my short answer...