So you mean like this

Normal
'If remember me selected
if RememberMe = "ON" then
'Writing cookies permanently
Response.Cookies("UserName")=UserName
Response.Cookies("Password")=Password
Response.Cookies("UserName").Expires = Now() + 365
Response.Cookies("Password").Expires = Now() + 365
Response.Redirect "welcome.asp"
else
'writing cookies temporarily
Response.Cookies("UserName")=UserName
Response.Cookies("Password")=Password
Response.Redirect "welcome.asp"
end if

My version
'If remember me selected
if RememberMe = "ON" then
'Writing cookies permanently
Response.Cookies("UserName")=test
Response.Cookies("Password")=test
Response.Cookies("UserName").Expires = Now() + 365
Response.Cookies("Password").Expires = Now() + 365
Response.Redirect "test.asp"
else
'writing cookies temporarily
Response.Cookies("UserName")=test
Response.Cookies("Password")=test
Response.Redirect "test.asp"
end if