New, tricyclic compounds containing a sulfonyl moiety in their structure, as potential safer COX inhibitors, were designed and synthesized. New derivatives have three conjugated rings and a sulfonyl group. A third ring, i.e., an oxazine, oxazepine or oxazocin, has been added to the 1,2-benzothiazine skeleton. Their anti-COX-1/COX-2 and cytotoxic effects in vitro on NHDF cells, together with the ability to interact with model membranes and the influence on reactive oxygen species and nitric oxide, were studied. Additionally, a molecular docking study was performed to understand the binding interaction of the compounds with the active site of cyclooxygenases. For the abovementioned biological evaluation of new tricyclic 1,2-benzothiazine derivatives, the following techniques and procedures were employed: the differential scanning calorimetry, the COX colorimetric inhibitor screening assay, the MTT, DCF-DA and Griess assays. All of the compounds studied demonstrated preferential inhibition of COX-2 compared to COX-1. Moreover, all the examined tricyclic 1,2-thiazine derivatives interacted with the phospholipid model membranes. Finally, they neither have cytotoxic potency, nor demonstrate significant influence on the level of reactive oxygen species or nitric oxide. Overall, the tricyclic 1,2-thiazine derivatives are good starting points for future pharmacological tests as a group of new anti-inflammatory agents.