If the students are in different forms and year groups, you can create a Static Group for them in Data Digger (Reporting>Data Digger).
Click on Manage Static Groups at the bottom of the screen and input the names of these students, giving the Group a name.
You can then run the Emergency Contacts report for this group (Reporting>Reports>Emergency Contacts).
Your Static Group will appear under the Group dropdown menu.
See -
Using Data Digger for creating a Dynamic Group or Static Group of students