Usually you can do the predictions in JAGS.  Below is a regression example with FEV (something to do with lung capacity) as the dependent variable and age and smoking indicator as predictors.  

FEV20s and FEV20ns are the predicted FEV values for a 20 year old smoker and a 20 year old non-smoker.

    model
    {
    for(i in 1:n){
    	FEV[i] ~ dnorm(mu[i],tau)
    	mu[i] <- beta[1] + beta[2]*Age[i] + beta[3]*Smoke[i]  + beta[4]*Age[i]*Smoke[i]
    }
    
    #priors
    beta[1] ~ dnorm(0,0.001)
    beta[2] ~ dnorm(0,0.001)
    beta[3] ~ dnorm(0,0.001)
    beta[4] ~ dnorm(0,0.001)
    tau ~ dgamma(0.001,0.001)
    sigma<-1/sqrt(tau) 
    
    ## Predict the FEV for a 20 year old smoker and for a 20 year old nonsmoker
    mu20s <-  beta[1] + (beta[2]+beta[4])*20 + beta[3]
    mu20ns <-  beta[1] + beta[2]*20 
    FEV20s ~ dnorm(mu20s,tau)
    FEV20ns ~ dnorm(mu20ns,tau)
    }