Turned the air blue

• Talked X-ratedly?
• Was bleeped on TV
• Crossed one's heart, e.g
• Took an oath in court
• Declared under oath
• Talked like a sailor, stereotypically
• Testified under oath
• Said with one's hand on a stack of Bibles
• Said some bad words

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Swear \Swear\, v. i. [imp. Swore , formerly Sware ; p. p. Sworn ; p. pr. & vb. n. Swearing .] [OE. swerien, AS. swerian; akin to D. zweren, OS. swerian, OHG. swerien, G. schw["o]ren, Icel. sverja, Sw. sv["a]rja, Dan. sv[ae]rge, Icel. & Sw. svara to answer, ...