How to not repeat code within catch blocks?

Create an interface:

public interface EntityManagerAction {
   public void execute(EntityManager em);
}

And a utility class:

public class EntityUtil {
  public static void executeWithEntityManager(EntityManagerAction action) {
    EntityManager em = someHowCreateEntityManager();

    EntityTransaction tx = null;
    try {
        action.execute(em);
        tx = em.getTransaction();
    } catch (RuntimeException e) {
        if (tx != null && tx.isActive()) { 
            tx.rollback();
        }
        throw e;
    } finally {
        em.close();
    }
  }
}

Now you can re-use the boiler-plate in the EntityUtil class, and your code becomes:

public SomeEntity doSomething (String someAttribute, String anotherAttribute) {
   Something something; 
   EntityUtil.executeWithEntityManager(new EntityManagerAction() {
        public void execute(EntityManager em ) {

        /*
         * ... independent logic ...
         */
         //use the passed in 'em' here.
        }
    });

    return something;
}

See also What is the “Execute Around” idiom?