Del. Code tit. 10, § 5108

In any proceeding before a judge, the Chancellor, or Vice-Chancellor, out of court, there may be allowed for the service of process or the attendance of witnesses a reasonable fee, not exceeding what is allowable for like service or attendance in proceedings before a justice of the peace. The judge, Chancellor, or Vice-Chancellor may make such order for the payment thereof as he or she considers just, and enforce obedience by attachment.