In my experience a typical search query doesn't generally map seamlessly one-to-one to a result, as you're describing. Even if you ask them to enter an order Id, they might want to be able to enter a partial ID and choose from a list, or they might mis-type (and you'd want to be able to give a meaningful response with possible choices, whereas an incorrect GET call to a resource that doesn't exist should just be a 404).
What I like to do is have an intermediate resource called something like SearchResult (it doesn't have to be an actual object in your system). Then my search query is a create call to /myapp/searchResults/ that includes the query parameters as POST variables. If the search result created points to a single order, than you can redirect to /orders/741, but if not, you have more ability to handle it.