1) Break your patterns. Reconnect with what you saying by breaking you vocal patterns. There's actually two ways to do this. One, is where you explore all the different ways you can say a line and still stay true to your choices. The other, is to do it more arbitrarily. Really, just go up where you went down, speak quickly where you spoke slowly, etc. This'll shake things up, and keep you present and playing. If you've been doing a monologue for a long time or it's just hard for you to break the patterns; start early - right away.
2) Drop the accent/character voice for a go of it. Speak with your own natural voice for a go. Be your own bullshit meter here. You'll immediately connect on a personal level. You'll get a sense very quickly of where you hold your tension too.
3) Find a person in your own life that parallels the character that you're speaking to. Insert that person's name- liberally. All sorts of great stuff will be triggered. Try different, appropriate people to see what effect it has.
Don't worry about being good or right. That actually should be kept in mind always when rehearsing! Don't practice; rehearse. Re-hear, or hear it a different way. Keep it fresh!