This paper presents a new approach called the backup path cost estimation (BPCE) for calculating the service (working) path in the online restoration problem. The objective of BPCE is to increase bandwidth efficiency and reduce the number of blocked requests in limited capacity networks. We propose two new algorithms that combine the BPCE approach with an existing restoration algorithm called shortest path local optimization (SPLO). One of the algorithms called BPCE-SPLO aims to reduce the total bandwidth requirement of the service path and the backup paths. The second algorithm called biased-SPLO aims to reduce the backup bandwidth requirement only. Both BPCE-SPLO and biased-SPLO have polynomial-time complexity. A comparative analysis is used to evaluate the performance of BPCE-SPLO and biased-SPLO. For the comparison, we include another known polynomial-time algorithm. Results have shown that BPCE-SPLO has a slightly lower total bandwidth requirement and has a significantly lower number of blocked requests in limited capacity networks than the other algorithms.