1.) The most effective thing you can do is pray...not just for yourself and your motives, but pray for the person you have offended that God would soften their heart towards you. God is in the business of mending relationships...so pray!
2.) Have patience...everyone works on their own time table. You may think the situation should have been over a long time ago, but that may not be the case for the other person. When a fence is broken...it takes some time to mend it...same is true with a relationship.
3.) Along that same line...don't try to force the situation. I've learned the hard way at times in my life...trying to force a reconciliation can do more damage than good...just keep praying and being patient.
4.) Don't continue to apologize...apologizing one time is enough. But, showing that you love and care is something that you should never stop doing. Be encouraging but never pushy.
Just stay in that place of forgiveness...keeping your life where it should be with your Maker.
Hope this helps you as much as typing it helped me.