Worthy to receive the Lord's Supper?

What does it mean to examine your heart before eating of the bread and drinking of the cup and, in so doing, what do you find? Is it a morbid introspection?  Are we to look for evidences of moral improvement and faithfulness which recommend us to the table?  Do we hope to find some assurance within that we are worthy to receive his food?  John Calvin writes:

By this, as I understand, he means that each individual should descend into himself; and consider, first, whether, with inward confidence of heart, he leans on the salvation obtained by Christ, and with confession of the mouth, acknowledges it; and, secondly, whether with zeal for purity and holiness he aspires to imitate Christ; whether, after his example, he is prepared to give himself to his brethren, and to hold himself in common with those with whom he has Christ in common; whether, as He himself is regarded by Christ, he in his turn regards all his brethren as members of his body, or, like his members, desires to cherish, defend, and assist them, not that the duties of faith and charity can now be perfected in us, but because it behooves us to contend and seek, with all our heart, daily to increase our faith. [Calvin's Institutes, Book 4:17:40]

He continues by reminding us of that bottom line which should never be forgotten, i.e. the good news of this feast:

Let us remember that this sacred feast is medicine to the sick, comfort to the sinner, and bounty to the poor; while to the healthy, the righteous, and the rich, if any such could be found, it would be of no value. For while Christ is therein given us for food, we perceive that without him we fail, pine, and waste away just as hunger destroys the vigor of the body. Next, as he is given for life, we perceive that without him we are certainly dead. Wherefore, the best and only worthiness which we can bring to God, is to offer him our own vileness, and, if I may so speak, unworthiness, that his mercy may make us worthy; to despond in ourselves, that we may he consoled in him; to humble ourselves, that we may be elevated by him; to accuse ourselves, that we may be justified by him; to aspire, moreover, to the unity which he recommends in the Supper; and, as he makes us all one in himself to desire to have all one soul, one heart, one tongue. If we ponder and meditate on these things, we may be shaken, but will never be overwhelmed by such considerations as these, how shall we, who are devoid of all good, polluted by the defilements of sin, and half dead, worthily eat the body of the Lord? We shall rather consider that we, who are poor, are coming to a benevolent giver, sick to a physician, sinful to the author of righteousness, in fine, dead to him who gives life... [Calvin's Institutes, Book 4:17:42]