A growing number of people are using catch-up TV services rather than watching simultaneously with other audience members at the time of broadcast. However, computational support for such catching-up users has not been well explored. In particular, we are observing an emerging phenomenon in online media consumption experiences in which speculation plays a vital role. As the phenomenon of speculation implicitly assumes simultaneity in media consumption, there is a gap for catching-up users, who cannot directly appreciate the consumption experiences. This conversely suggests that there is potential for computational support to enhance the consumption experiences of catching-up users. Accordingly, we conducted a series of studies to pave the way for developing computational support for catching-up users. First, we conducted semi-structured interviews to understand how people are engaging with speculation during media consumption. As a result, we discovered the distinctive aspects of speculation-based consumption experiences in contrast to social viewing experiences sharing immediate reactions that have been discussed in previous studies. We then designed two prototypes for supporting catching-up users based on our quantitative analysis of Twitter data in regard to reaction- and speculation-based media consumption. Lastly, we evaluated the prototypes in a user experiment and, based on its results, discussed ways to empower catching-up users with computational supports in response to recent transformations in media consumption.