Older adults with a chronic health condition (e.g. hypertension) use various self-management methods. Healthcare technologies have the potential to support health self-management. However, it is necessary to understand the acceptance of these technologies as a precursor to older adults’ adoption and integration into their health plan. Our focus was on the factors older adults with hypertension initially consider when introduced to three new healthcare technologies that might support their health self-management. We compared their considerations for a blood pressure monitor, an electronic pillbox and a multifunction robot to simulate incrementally more complex technologies. Twenty-three participants (aged 65–84) completed four questionnaires and a semi-structured interview. The interview transcripts were analysed using a thematic analysis approach. We identified the factors that were frequently mentioned among the participants for each of the three healthcare technologies. The factors that older adults initially considered were familiarity, perceived benefits, perceived ease of use, perceived need for oneself, relative advantage, complexity and perceived need for others. Upon further reflection, participants considered advice acceptance, compatibility, convenience, facilitating conditions, perceived usefulness, privacy, subjective norm, and trust. We integrated the factors that older adults considered into the Healthcare Technology Acceptance Model (H-TAM), which elucidates the complexity of healthcare technology acceptance and provides guidance for future explorations.