You should explain clearly what kind of raw data you have, and how did you assemble the draft genome. I will assume you only have Illumina paired-end reads and assembled the genome using just this data with any unknown short read genome assembler.

Your problem is not so simple, because unless you have a very high quality assembly (which I assumed you don't), the contigs should be really fragmented and even the mitochondrial genome hasn't been assembled into a single contig.

Create a blast database from your assembly, then use blast with the reference mitogenome as query and the draft genome as database to search for contigs with similarity to the reference mitogenome. Due to the fragmented state of your assembly and the possible existence of NUMTs, you will get more hits than you would like. Now you can either blast these contigs against NCBI NT, or you can try to assemble these contigs with CAP3, and then blast against NT. If you are lucky, you will get just one contig with high similarity over the whole sequence and of the appropriate length.