Del. Code tit. 11 § 4502
No writ of error or writ of certiorari issuing from the Supreme Court in any criminal cause shall operate as a stay of execution of the sentence of the trial court unless such writ of error or writ of certiorari be sued out within 30 days from the date of final judgment in the court below, and unless the plaintiff in error obtains from the trial court (or, if the trial court refuses, then from 1 of the Justices of the Supreme Court) a certificate that there is reasonable ground to believe that there is error in the record which might require a reversal of the judgment below, or that the record presents an important question of substantive law which ought to be decided by the Supreme Court, and unless the plaintiff in error furnishes bond to the State, with surety to be approved and in an amount to be fixed by 1 of the Justices of the Supreme Court, conditioned as prescribed by rule of court. In cases where sentence of life imprisonment has been imposed, there shall be no stay of execution, and no supersedeas bond taken or allowed. In cases where sentence of death has been imposed, the trial court, if the certificate provided for in this section has been granted, may stay the execution of the death penalty pending the determination of the cause by the Supreme Court, but the defendant below shall not be released from custody.
11 Del. C. § 4502