The other day I had a wonderful answer to prayer, for a dying relative. I asked for her pain to taken away on her last day, and for God to reveal himself to her. And that day, to the surprise of her doctor and nurses, she was completely pain-free and lucid as the end came. Just before the end, she slept for a while, and woke up greatly changed in outlook, like a new person.
I don't know what happened while she slept, although another person praying for her at a distance went through a real spiritual struggle of intense feelings and sensations, followed by joy and peace.
When we pray for a particular thing, sometimes I think that God gives us a some tangible sign of his hand accompanying the answer - an outward sign to assure us that the less tangible matter has also been heard. It is like Jesus' response to the paralysed man - to show that the harder, but intangible thing has been given ("your sins are forgiven"), the outward healing is shown ("get up, take up your mat and walk").
The English Puritan Thomas Goodwin knew about this way God answers some prayers: "When God doth a thing in answer to prayers, he often doth it in such a manner, that his hand may be in a more than ordinary manner seen in it. . . .there is often some particular circumstance of providece concurrent with it, which is a token for good, and sealeth to us that it is from God. . ." (The Return of Prayers).
The Lord has sealed this answer for me this week, his Name is wonderful.