I'm going to have to disagree on this one with both Calvinists, on the one hand, and Arminians, Catholics, and Orthodox on the other.
I don't believe, as Calvinists do (or at least Calvinists in the Puritan and Dutch Reformed traditions) that we should look for signs of our election, whether an inner peace or sense (as the hymn says) or in our actions (Pietism). I don't believe we can find complete assurance in them.
However, I do believe- and this is a particularly Lutheran way of looking at it- that we can find complete assurance in the sacraments, because God has sealed visible signs with the power of his gracious, ever-present word. We are identity as adopted children of God in baptism, and that fundamentally marks us out as saved. We hear our baptized status affirmed and renewed in the absolution proclaimed whenever we repent, even if our repentance is imperfect. And we partake in the eschatological judgment when partaking of Christ's body and blood, and pass through that judgment to participate in the marriage feast of the lamb in his kingdom.
What more assurance could we possibly want or need? If we believe that God has sealed and signed these visible elements to his gracious promise of forgiveness, and that through them he imparts to us his very own nature and makes us one with him, then I assert that we cannot possibly have more assurance of our salvation.
I may be overstating my case a little, since I do not believe in the perseverance of the saints, nor do I believe that every recipient is a faithful recipient. However, if we do receive faithfully, and continue to receive faithfully, then we have already received and are still regularly receiving the adoption, forgiveness, and final favorable judgment which will be made visibly manifest at the parousia.