It's easy just create two connection strings.
example:
public int GetId(){
using (SqlConnection con = new SqlConnection("CONNECTION STRING TO CUSTOMER DB")
{
}
}
public void Save(int customerId, object Quote){
using (SqlConnection con = new SqlConnection("CONNECTION STRING TO QUOTE DB")
{
}
}
If you need to do it in transaction I recommend you to read some articles about that.
A Beginner's Tutorial for Understanding Transactions and TransactionScope in ADO.NET[
^]
You are interested in distributed transactions.