This paper proposes the base station ordering localization technique (BoLT) for emergency call localization in cellular networks. Exploiting the foreseen ultra-densification of the next-generation (5G and beyond) cellular networks, we utilize higher-order Voronoi tessellations to provide ubiquitous localization services that are in compliance to the public safety standards in cellular networks. The proposed localization algorithm runs at the base stations (BSs) and requires minimal operation from agents (i.e., mobile users). Particularly, BoLT requires each agent to feedback a neighbor cell list (NCL) that contains the order of neighboring BSs based on the received signal power in the pilots sent from these BSs. Moreover, this paper utilizes stochastic geometry to develop a tractable mathematical model to assess the performance of BoLT in a general network setting. The goal of this paper is to answer the following two fundamental questions: i) how many BSs should be ordered and reported by the agent to achieve a desirable localization accuracy? and ii) what is the localization error probability given that the pilot signals are subject to shadowing? Assuming that the BSs are deployed according to a Poisson point process (PPP), we answer these two questions via characterizing the tradeoff between the area of location region (ALR) and the localization error probability in terms of the number of BSs ordered by the agent. The results show that reporting the order of six neighboring BSs is sufficient to localize the agent within 10% of the cell area. Increasing the number of reported BSs to ten confines the location region to 1% of the cell area. This would translate to the range of a few meters to decimeters in the foreseen ultra-dense 5G networks.