C# - Get Item From Collection By Unique ID

I have a collection of Contacts that inherits from CollectionBase:

public class ContactCollection : CollectionBase{
//...
}

each contact in the collection has a unique ID:

public class Contact{
public int ContactID{
get;
private set;
}
//...
}

I think what I would like to do is something like the following:

// get the contact by their unique [Contact]ID
Contact myPerson = Contact.GetContactById(15);
// get all contacts for the customer
ContactCollection contacts = customer.GetContacts();
// replaces the contact in the collection with the
// myPerson contact with the same ContactID.
contacts.ReplaceAt(myPerson);
// saves the changes to the contacts and the customer
// customer.Save();