We equip a recently developed model for the specification of service contracts with real-time constraints. Service contracts offer a means to define the behavioural compliance of a composition of services, typically dictated in a Service-Level Agreement (SLA), as the fulfilment of all service requests through service offers. Depending on their granularity, SLAs vary according to the level of criticality of the involved services and also contain real-time aspects, like the services' response or expiration time. A standard method to refine a spurious service composition into a compliant one is via the synthesis of a safe orchestration, in the form of the most permissive controller from Supervisory Control Theory (SCT). Ideally, safe orchestrations solve competition among matching service requests and offers, in light of their criticalities and their timing constraints, in the best possible way. In this paper, we introduce timed service contract automata as a novel formal model for service contracts with real-time constraints on top of services with varying levels of criticality. We also define a means to efficiently compute their composition and their safe orchestration, using the concept of zones from timed games. The innovations of our contribution are illustrated by intuitive examples and by a preliminary evaluation.