Do you use MDI or a pump? If you pump, then adjust your basal overnight. If MDI, consider splitting your dose into morning and night doses so you have a higher basal during the night, or changing to Levemir which is taken twice a day and so allows more basal fine tuning (obviously consult your doctor first). Some people also find eating a small snack before bed can help with this.
Also, if this was just a once off, it may be sickness/bad site/last night's dinner/a million other things, so make sure you see a trend of highs before you decide this is dawn phenomenon.