Lewis & Short

ob-testātĭo, ōnis, f. [obtestor],

  1. I. an adjuring, conjuring; an engaging or obliging to any thing by calling God to witness (class.): obtestatio est, cum deus testis in meliorem partem vocatur: detestatio, cum in deteriorem, Paul. ex Fest. p. 184 Müll.: quid ergo illa tua obtestatio tibicinis? Cic. Dom. 48, 125: viri, Cic. Clu. 12, 35; id. Balb. 14, 33.
  2. II. Transf., an earnest entreaty, adjuration (rare); in plur.: matronae in preces obtestationesque versae, supplications, Liv. 27, 50: senatus ad infimas obtestationes procumbens, Tac. A. 1, 12: quā obtestatione discedens, Cael. ap. Cic. Fam. 8, 10, 5; Cic. Fam. 13, 1, 4; Suet. Tib. 40.