The need for battlefield digitization, coupled with the growing demand for transporting diverse and bandwidth intensive applications both in the military and commercial sectors, have led to a rapid growth in broadband networks. The success of these broadband networks, however, is critically tied to their robustness. We propose and study two restoration strategies to restore the affected connections in the event of network facility failures in broadband ATM networks. The restoration strategies are characterized by the fact that they use the untapped resources of the underlying network rather than relying on dedicated backup. Such strategies will not only help in providing cost-effective network solutions for robustness in commercial communications networks, but will also be very useful in a scenario with diminishing network resources such as a battlefield. In a battlefield, the network elements such as switches and/or links can fail sporadically due to hostile conditions, causing a decrease in the available resources. Further, the proposed restoration strategies operate on a connection-by-connection basis thereby allowing network operators to provide a high degree of robustness for mission critical and premium service applications, and a comparatively lower degree of robustness to low priority applications depending on their specific QoS requirements.