Larry raised good points, but Ensembl compara does have this pre-computed. The Ensembl team members on this forum may give more details on how they accomplish this.
I use BioMart to access this data (link at top of the ensembl page):
Dataset: Homo sapiens genes Filter: -> Gene -> Gene type : miRNA Attributes -> Gene -> Ensembl (check where required) Attributes -> Homologs -> ORTHOLOGS -> Mouse Orthologs (check where required)
I think that it is very telling that NCBI does not have homologous/orthologous genes pre-determined for microRNA genes, as they do for protein-coding genes. To me, this implies two important aspects of microRNA biology and gene conservation.
One, the sequences are short, especially the functional domain of a miR, and so detection of conservation may not be reliable. Keep in mind that introns of protein-coding genes, which typically serve no function, from mouse and human do not align so well.
Two, conservation really depends on the miR-mRNA interaction - meaning that functionality across mouse to human may not be conserved if the mouse miR regulates a whole set of genes that are different from those in human - with the miR of the same name.
Thus, to find such conservation, I would look for the degree to which validated miR-mRNA pairs are conserved in the two organisms. I realize this is a much tougher nut to crack, but will give a list of microRNAs of much higher confidence for experiments based on this bioinformatics activity.
Targetscan uses the UCSC alignments to determine conservation across mammals for miRs. Also, they have downloadable files of miRs that are non-conserved vs conserved, based on this data.
You may also look to microrna.org which uses the same conservation scheme, but offers a phascon score as an additional measure of conservation.
You can guide your inquiry by starting with the highly conserved miR lists, as these will likely have many miRs conserved between human and mouse.
The following is taken form the Targetscan website:
TargetScan predicts biological targets of miRNAs by searching for the presence of conserved 8mer and 7mer sites that match the seed region of each miRNA (ref. 1). As an option, nonconserved sites are also predicted. Also identified are sites with mismatches in the seed region that are compensated by conserved 3' pairing (ref. 3). In mammals, predictions are ranked based on the predicted efficacy of targeting as calculated using the context scores of the sites (ref. 2). TargetScanHuman considers matches to annotated human UTRs and their orthologs, as defined by UCSC whole-genome alignments. Conserved targeting has also been detected within open reading frames (ORFs). A listing of these ORF sites can be found at the bottom of Supplemental Table 2 of reference 1.
References: 1) Conserved Seed Pairing, Often Flanked by Adenosines, Indicates that Thousands of Human Genes are MicroRNA Targets Benjamin P Lewis, Christopher B Burge, David P Bartel. Cell, 120:15-20 (2005).
2) MicroRNA Targeting Specificity in Mammals: Determinants beyond Seed Pairing
Andrew Grimson, Kyle Kai-How Farh, Wendy K Johnston, Philip Garrett-Engele, Lee P Lim, David P Bartel. Molecular Cell, 27:91-105 (2007).
3) Most Mammalian mRNAs Are Conserved Targets of MicroRNAs Robin C Friedman, Kyle Kai-How Farh, Christopher B Burge, David P Bartel. Genome Research, 19:92-105 (2009).
You can also try VIRmiRNA; where they have given MirAlign tool to Align miRNA seed sequence with their databse or with miRBase..!!
paste your seed seq of human miR in fasta format and select databse as "miRBase"..!!
for more info, please visit http://crdd.osdd.net/servers/virmirna/
VIRmiRNA: a comprehensive resource for experimentally validated viral miRNAs and their targets. Database (Oxford). 2014 Nov 7;2014. pii: bau103. doi: 10.1093/database/bau103. PMID: 25380780