If this lesson and assignment were part of a team effort (i.e. across your grade level team), you can gather together with your colleagues and grade the papers together. Often it is helpful to have another set of eyes and ears to to assist you in getting comfortable with a new rubric.
Additionally, you can arrange for each paper to be graded by two different teachers. Then the scores can be averaged or added together. This serves to corroborate the score and reinforce its meaning.